Proposal

for

The Undergraduate Program

 in

Actuarial Science and Financial Mathematics

 

 

 

 

 

 

by

Department of Mathematical Sciences

Department of Finance &

Department of Islamic and Arabic Studies

King Fahd University of Petroleum and Minerals

Dhahran

 


 

1.      Introduction

The development of sophisticated technology and new ideas of thinking due to the internet boom has modified in many ways the scope and nature of business as well as challenges arising from the on-site situation in the private sector. The roadmarks of the changes, challenges, and opportunities include

·        The general trend of high-tech production

·        Volatility of the stock market

·        Need to equip manpower with skills suited to cope and handle a wide range of complex financial, societal, economical, or industrial risks in an optimized manner

·        Increased demand of people who could efficiently model, analyze, and provide solutions to real-life financial, societal, economical, or industrial problems

·        Emergence of advanced mathematical and statistical methods as a vital component of Research and Development and an essential management factor in financial, societal, economical, or industrial sector

·        Unanticipated emergence of untapped financial businesses such as the Islamic banking system and the Takaful business

This in turn presents a challenge for the academic institutions to develop programs that would combine computational and analytic knowledge with modeling skills of real-life applications. Such a challenge, when confronted, has led to the evolution of Actuarial science programs at many well-known academic institutions in the world.

 

Keeping in mind the leading role of KFUPM to be at the cutting edge by pioneering research and academic activities related to contemporary progress worldwide, the Department of Mathematical Sciences in collaboration with Finance and Islamic and Arabic studies Departments is proposing a B.Sc. program in Actuarial Science and Financial Mathematics. The Program is designed to produce manpower with ample background for modeling, analyzing, solving, and managing financial and operational risks in the private and government sectors and industries of the country. There is currently no program of this sort at the University.

 

The term Actuary is not new; the Society of Actuaries (SOA), Casualty Actuarial Society (CAS), and Institute of Actuaries (IA) were established decades ago in North America and European countries. Soon after, many societies and foundations of Actuaries were established in many international countries. Today a large number of universities are offering programs to produce manpower which falls under this rapidly developing discipline. Over the past 5 years, the job almanac in the US rated Actuaries as the first among the top-paying careers in America. This is also true in other countries as well. Currently in Saudi Arabia, one of the top paying careers is “Financial Manager” whose main line of work is advising individuals and companies the best investments and the best time to invest. The intuitive investment skills a “Financial manager” uses to base these recommendations on are knowledge and skills an actuary acquires from a formal program like the one proposed here. In fact, an actuary is equipped with the financial, mathematical, and statistical knowledge to scientifically predict which investment is financially less risky, which produces the most investment yield, and at which time. There are several journals devoted to this area and there are numerous professional society-based online sources of activities and research and career support developments in this area.

 

2.      Objectives of the Proposed Program

Actuarial Science and Financial Mathematics is the science that manages risk in the financial and government sector and industries. Specifically, it is the science of analyzing risk data and making informed decisions from it. A combination of deterministic and stochastic approaches to managing risk is one main area of studyA graduate of the program is expected to contribute in all areas of Saudi Arabian financial sector and industry as well as the government sector where the objective of stochastic minimization of risk is the daily main focus. A graduate typically find employment in private and government sectors and industry that deals with investment, insurance, pension funding, business, financial consulting, marketing, manufacturing, healthcare funding, banking, and management of operational risks. An actuary is a professional who analyzes the financial consequences of risk. Actuaries use mathematics, statistics and financial theory to study uncertain future events, such as those of concern to insurance and pension programs and investment returns. They evaluate the likelihood of those events, design creative ways to reduce the likelihood and decrease the impact of adverse events that actually do occur. Actuaries are an important part of the management team of the companies that employ them. Their work requires a combination of strong analytical skills, business knowledge and understanding of human behavior to design and manage programs that control risk. An Actuary also minimizes daily operational risks in industry.  An actuary is a value asset in every institution that strives to minimize this risk. The input of the Actuary is essential for the success of every endeavor.

The objective of the BS program in Actuarial Science and Financial Mathematics  is to prepare students for career opportunities in government as well as the private sector in such fields as asset liability management, business, banking, investment, insurance or takaful, pension funding, financial consulting, healthcare funding, industry, and for further graduate studies. In addition, the program also prepares the students for international society examinations such as Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) exams P (Probability) and FM (Financial Mathematics). With an advanced undergraduate curriculum of study, as classified by Society of Actuaries for programs preparing students for at least these first two societal exams with topics covered for the third and fourth exams, a graduate of the program may have a stronger likelihood of employment in the private sector, industry, and government sector in Saudi Arabia and abroad. The program has a good balance of theory, applications and data analysis, as well as carefully selected sequences of courses from computer science, economics, accounting, finance, and management. This interdisciplinary approach is meant to make the program flexible, and give the students a broad base of education, thus, improving their chances of employment. Graduates of the program are well-qualified scientists with good knowledge in mathematics, probability, statistics, computing, economics, accounting, finance, and management.

 

 

3.      Significance to the Kingdom

The economic development of the kingdom has reached a high level of sophistication. A program in “Actuarial Science and Financial Mathematics ” will certainly enhance this development by providing manpower who not only understands the economic, societal, operational, and financial risks facing the country’s businesses but also know how best to advise them on the best course of action to minimize and manage these risks. In addition, this program will open up avenues for our graduates. Degree holders of this program will play a vital role in many organizations such as banking institutions, insurance or takaful companies, Financial consulting firms, commerce, social sector, investments, security trading, pension funding, healthcare funding, industry, national environmental risks agencies, national retirement planning, and national demography and census management.

 

4.      Significance for KFUPM

On the forefront, the output of the program seems to be centered on production of specialized skilled manpower with high ability to help the country’s businesses and organizations manage economic, operational, societal, and financial risks. Another important aspect of the program is the crucial part it plays in fostering interdisciplinary activities at KFUPM. The program, once launched, will create mutually beneficially link between the private and governmental sectors and the various departments at KFUPM, leading to more research collaborations of interdisciplinary nature. This can ultimately contribute in

·        Introducing challenging new research areas with a direct bearing on the development of interdisciplinary research at KFUPM.

·        Developing, jointly with several departments at KFUPM, new ideas and approaches of research of a multidisciplinary nature.

 

The role of mathematical sciences as a ground of all scientific disciplines and areas is widely recognized. Hence, it is only natural to emphasize its contribution in the development of new research avenues that cuts across disciplines.

 

5.      Degree to be awarded

Bachelor of Science in Actuarial Science and Financial Mathematics

 

6.      Availability of the resources

    1. Manpower

The Department of Mathematical Sciences has about twenty faculty members in Applied Mathematics, Numerical Analyses, Probability, and Statistics. Some of them can contribute in program instruction. Moreover, the interdisciplinary nature of the program and the presence of cross-listed courses in the program, faculty members from other departments are also expected to participate. However, given the more specialized Actuarial major courses, the program may need faculty with some specialized Actuarial training to teach these courses. Currently, the Department of Mathematical Sciences has only one faculty member who was trained as an Actuary and a Statistician with specialization in educational measurement and testing and another faculty member with training in Statistics and whose research area is Stochastic Process. The Department of Finance has some faculty members currently teaching the required finance courses such as Investments course and Risk Management and Insurance course. However, currently there are no faculty members with specialization or training in Islamic Finance. At present, there are more courses than there are faculty members with training or specialization in areas supportive of the program courses. So, there is a need to add faculty members with specialization in line with this program. On the whole, the program is estimated to need at least four new faculty members to teach all the proposed new courses.

    1. Research and Teaching Facilities

Several computer laboratories are available ranging from PCs to servers running under different operating systems. These laboratories, scattered across campus, are under the supervision of the ITC. The Department of Mathematical Sciences has a PC Lab with forty networked machines. The College of Industrial Management has two PC labs with around thirty and around forty networked machines. The program will, therefore, need a minimum of other computing facilities, mainly regarding parallel computation that is now available at a reasonable cost. In addition, the Actuarial Programming Language (APL) software will also be needed.

    1. Main Library

The main library is well equipped in terms of scientific and engineering literature. However, some Actuarial-related books especially those recommended by international society of actuaries, Actuarial-related journals, and conference proceedings on Islamic Finance or similar conference proceedings will need to be ordered for references.

7.      Rationale for the contents of courses

The curriculum development for this program is focused on providing an enriched sequence in which analytic, stochastic modeling, and computation techniques for real-world economic, operational, societal and financial problem solving are synthesized. The design of course content is based on a careful selection of topics relevant to the needs of the private and governmental sectors and industries of the Kingdom. Core courses provide the common basis needed to understand, analyze, model, and manage real-life social, operational, financial, and economic problems arising from different situations. They also provide specific stochastic tools to solve such problems. With the core courses, graduates of the program are well equipped with knowledge to work in any sector that uses actuarial and financial optimization skills.

The program is also structured to offer electives from a wide range of courses integrating modern stochastic tools with practice. Some of the electives are of true multidisciplinary nature. This versatility will equip graduates of the program, contingent on their choice of elective, with capabilities of working in diverse areas of Saudi institutions.

For instance, with the indicated choice of electives, the graduates of the program can apply their skills as a specialist or team member in the following sectors.

·        Banking

With the core courses and the listed elective courses below, a graduate will be a financial optimization scientist or specialist working in the Banking industry. He will be equipped with knowledge on financial transactions in the banking industry as well as the actuarial skills to manage banking-related risks.

o       IAS 421, FIN 421, STAT 461, ECON 305, FIN 410, FIN 425

·        Chambers of Commerce

With the core courses and the listed elective courses below, a graduate will be a financial optimization scientist or specialist working in the Chambers of Commerce.  He will be equipped with knowledge on financial transactions in business as well as the actuarial skills to advise the Chamber on regulating commerce-related risks.

o       IAS 421, FIN 421, STAT 461, MGT 301, ECON 305

·        Investments

With the core courses and the listed elective courses below, a graduate will be a financial optimization scientist or specialist working in speculating returns and risks related to investments.  He will be equipped with knowledge on financial transactions in investments as well as the actuarial skills to minimize investment-related risk, model stock market data, predict the next time stock prices are expected to rise or decline, and maximize investors’ investment returns.

o       IAS 421, FIN 421, STAT 461, MATH 485, FIN 425, MATH 301

·        Financial Consulting

With the core courses and the listed elective courses below, a graduate will be a financial optimization scientist or specialist working in the Financial Consulting industry. He will be equipped with knowledge on financial transactions in the business as well as the actuarial skills to manage financial-related risk as well as conduct feasibility studies on financial projects. With these skills, he would be a very important team member in a financial consulting firm.

o       IAS 421, FIN 421, STAT 461, FIN 410, FIN 425, MATH 485

·        Financial securities management

With the core courses and the listed elective courses below, a graduate will function as a financial optimization scientist or specialist working in the financial securities management. He will be equipped with knowledge on financial transactions in the securities trading as well as the actuarial skills to manage financial-related risk on these security trading. With these skills, he would be a very important member in a financial security management team.

o       IAS 421, FIN 421, STAT 461, FIN 302, MGT 311

·        Asset and Fund management

With the core courses and the listed elective courses below, a graduate will function as a financial optimization scientist or specialist working in the Asset and Fund Management department in any company. He will be equipped with knowledge on financial fund and asset management as well as the actuarial skills to manage financial-related risk on these funds and asset. With these skills, he would be a key member of any company.

o       IAS 421, FIN 421, STAT 461, FIN 410

·        Healthcare funding

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the healthcare funding field. He will be equipped with knowledge on mortality rates as well as the actuarial skills to minimize the impact of mortality-related risk on society with adequate funding appropriation and maximize society’s readiness in terms of funding for the next occurrence of sickness. With these skills, he would be a very important member in a healthcare funding organization.

o       FIN 430, MATH 480, STAT 461, STAT 498

·        Pension Funding

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the pension funding field. He will be equipped with knowledge on mortality rates and finance as well as the actuarial skills to minimize the impact of mortality-related risks on an employer’s responsibility for adequate pension funding appropriation. With these skills, he would be a very important member in any company responsible for an attractive pension funding package for their employees.

o       FIN 430, STAT 498, STAT 461, STAT 355

·        Insurance and Takaful

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the conventional and Islamic (takaful) insurance field. He will be equipped with knowledge on mortality rates or accident rates and finance as well as the actuarial skills to minimize the impact of these risks on an insurer’s responsibility for adequate insurance or takaful funding appropriation.

o       IAS 420, FIN 430, STAT 355, STAT 461

·        National Insurance and Takaful Regulation

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the conventional and Islamic (takaful) insurance field. He will be equipped with knowledge on mortality rates or accident rates and finance as well as the actuarial skills to minimize the figure out and regulate the insurance premiums that are charged by insurance or takaful companies. A national insurance of takaful regulator will ensure that the monetary value of protection against risks is justified.

o       IAS 420, FIN 430, STAT 355, STAT 461, ECON 306

·        National Census and demography management

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the census and demography management of the country. He will be equipped with knowledge on various rates of the nation’s demography as well as the actuarial skills to manage demographic and census data, to project some future rates and to evaluate shifts in the current demographic rates to advise the government on the need for a new census.

o       FIN 430, STAT355, STAT 440, STAT 365

·        National Environmental Risk Agency

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the Environmental Risk Agency of the country. He will be equipped with knowledge on risks related to the environment on the set-up of a new business or company and the actuarial skills to forecast the impact of these environmental risks. With this information, he can advise the governmental agency on the impact of these environmental risks.

o       FIN 430, STAT 461, MATH 472, STAT 440

·        Operational Risk Management for Industries

With the core courses and the listed elective courses below, a graduate will function as a scientist or specialist working in the country’s industries on managing daily risks in their operation. For example, the expected on-the-job risks of different techniques of the operation of drilling oil to employees at ARAMCO can be calculated by an actuary so that these risks can be kept to the minimum. Also, the probability models for drilling oil can be developed and used by an actuary to maximize oil productions.  With this information, he can advise the company what is the best option for each company’s operation.

o       FIN 430, STAT 461, MGT 311, STAT 325, STAT 430

 

 


 

 

ACTUARIAL SCIENCE AND FINANCIAL MATHEMATICS MAJOR

 

Objective of the Program

 

Actuarial Science and Financial Mathematics is the science that manages risk in the financial and government sector and industries. Specifically, it is the science of analyzing risk data and making informed decisions from it. A combination of deterministic and stochastic approaches to managing risk is one main area of studyA graduate of the program is expected to contribute in all areas of Saudi Arabian financial sector and industry as well as the government sector where the objective of stochastic minimization of risk is the daily main focus. A graduate typically find employment in private and government sectors and industry that deals with investment, insurance, pension funding, business, financial consulting, marketing, manufacturing, healthcare funding, banking, and management of operational risks. An actuary is a professional who analyzes the financial consequences of risk. Actuaries use mathematics, statistics and financial theory to study uncertain future events, such as those of concern to insurance and pension programs and investment returns. They evaluate the likelihood of those events, design creative ways to reduce the likelihood and decrease the impact of adverse events that actually do occur. Actuaries are an important part of the management team of the companies that employ them. Their work requires a combination of strong analytical skills, business knowledge and understanding of human behavior to design and manage programs that control risk. An Actuary also minimizes daily operational risks in industry.  An actuary is value asset in every institution that strives to minimize this risk. The input of the Actuary is essential for the success of every endeavor.

 

The objective of the BS program in Actuarial Science and Financial Mathematics  is to prepare students for career opportunities in government as well as the private sector in such fields as asset liability management, business, banking, investment, insurance or takaful, pension funding, financial consulting, healthcare funding, industry, and for further graduate studies. In addition, the program also prepares the students for international society examinations such as Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) exams P (Probability) and FM (Financial Mathematics). With an advanced undergraduate curriculum of study, as classified by Society of Actuaries for programs preparing students for at least these first two societal exams with topics covered for the third and fourth exams, a graduate of the program may have a stronger likelihood of employment in the private sector, industry, and government sector in Saudi Arabia and abroad. The program has a good balance of theory, applications and data analysis, as well as carefully selected sequences of courses from computer science, economics, accounting, finance, and management. This interdisciplinary approach is meant to make the program flexible, and give the students a broad base of education, thus, improving their chances of employment. Graduates of the program are well-qualified scientists with good knowledge in mathematics, probability, statistics, computing, economics, accounting, finance, and management.

 

 

 

 

 


 

REQUIREMENTS FOR THE B.S. DEGREE IN 

ACTUARIAL SCIENCE AND FINANCIAL MATHEMATICS

 

General Education Requirements (62 credit hours)                        Credit Hours

English

ENGL 101, 102

6

Communication Skills

ENGL 214

3

 

IAS 101, 201, 301

6

Islamic & Arabic Studies

IAS 111, 211, 311

6

Physical Education

PE 101, 102

2

Mathematics

MATH 101, 102, 131FM,P*, 201, 280

17

Natural Sciences

CHEM 101 or PHYS 101 or 133

4

Social and Behavioral Sciences

ECON 101VE, 102VE

6

Computer Programming

ICS 102

3

Accounting and Finance

ACCT 201VF, ACCT 202VF,

FIN 301VF

9

 

 

62

Major requirements (44 credit hours)

Pre-requisite requirements (9 credits)

Introduction to Numerical Computing (for Actuaries)C

MATH 321 (modified)

3

Introduction to Statistics VS

STAT 201

3

Business Statistics II* VS

STAT 212 (modified pre-requisite)

3

Core requirements (35 credits)

Introduction to Probability Theory*P

STAT 301

3

Statistical Inference

STAT 302

3

Regression AnalysisVS

STAT 310

3

Time SeriesVS

STAT 460

3

Financial Mathematics*FM

New Course (STAT 280)

3

Life Contingencies IM

New Course (STAT 381)

3

Life Contingencies IIM

New Course (STAT 482)

3

Stochastic Processes (for Actuaries)M

STAT415 (modified)

3

Survival Models for ActuariesM

STAT 475 (modified)

3

InvestmentsVF

FIN 420

3

Actuarial Risk Theory and CredibilityC

New Course (STAT 483)

3

Actuarial Science Problem Labs

New Course (STAT 488)

2 (1 cr ea)

 

 

44

Major Electives (12 credit hours)

Risk Management and InsuranceC

FIN 430

3

Intro to Islamic Insurance (Takaful)

New Course (IAS 420)

3

Intro to Islamic Finance

New Course (IAS 421)

3

Security Analysis and Portfolio Management

FIN 421

3

Operations Research I

STAT 361

3

Demographic Methods

STAT 355

3

Topics in Actuarial Science (Graduation theory, Advanced Risk Theory, Simulation Methods, or other advanced topics)

New Course (STAT 498) with variable content

3

Numerical Analysis II

MATH 472

3

Operations Research II

STAT 461

3

Wavelets and Applications

MATH 485

3

Linear & Nonlinear Programming

MATH 480

3

Methods of Applied Math

MATH 301

3

Advanced Calc I

MATH 311

3

Advanced Calc II

MATH 411

3

Advanced Calc III

MATH 412

3

Intro to Measure Theory & Functional Analysis

MATH 431

3

Multivariate Analysis

STAT 440

3

Linear Models

STAT 435

3

Numerical Analyses I

MATH 471

3

Money and Banking

ECON 305

3

Financial Management II

FIN 302

3

International Financial Management

FIN 410

3

Computer Applications in Finance

FIN 425

3

Nonparametric Statistical Methods

STAT 325

3

Data Collection and Sampling Methods

STAT 365

3

Experimental Design

STAT 430

3

Graph Theory

MATH 425

3

Principles of Marketing

MKT 301

3

Principles of Management

MGT 301

3

Legal Environment

MGT 311

3

Economy of Saudi Arabia

ECON 306

3

With the core courses, students are well qualified for careers in General Actuarial practice. For more specific tracks, students are advised to take at least the following major electives:

·        Insurance and Takaful Track

o       IAS 420, FIN 430

·        Financial Optimization Track

o       IAS 421, FIN 421

·        Operational Risk Management Track

o       FIN 430, STAT 461

Free Electives (6 credit hours)

 

Summer Training (2 credit hours)

Students are required to spend one summer working in industry prior to the term in which they expect to graduate. It is recommended that students attempt to take their first Society of Actuaries exam (exam P) after completing their STAT 488 course and prior to the summer training to increase their likelihood of employment in the industry.

 

Total Requirements (126 credit hours)

The B.S. degree in Actuarial Science and Financial Mathematics requires a minimum total of 126 credit hours.


 

Actuarial Science and Financial Mathematics Course Description

 

STAT 280 Financial Mathematics                                                                           3-0-3

The course concentrates on the theory of compound interest and the mathematics of investment and credit; however, life contingencies are also introduced toward the end of the semester. Major topics include the measurement of interest, annuities certain (level, non-level, and continuous), amortization schedules, sinking funds, investment yield rates, and bonds.  A basic knowledge of calculus and probability is assumed.  This course is intended for Actuarial Science and Financial Mathematics  majors who are studying for the professional exam on Financial Mathematics (FM) given by the Society of Actuaries and the Casualty Actuarial Society.

Prerequisites:   MATH 102 and MATH 131

Suggested Reference:

  1. Broverman, S.A. 1996. Mathematics of Investment and Credit (2nd ed.). Connecticut: ACTEX Publications.
  2. Kellison, S.G. 1991. Theory of Interest (2nd ed.). Homewood: Irwin.
  3. Society of Actuaries Study Notes for Professional Exam FM or ACTEX study Manual 140.

 

STAT 381 Life Contingencies I                                                                                3-0-3

This course is an introduction to life insurance mathematics based on a stochastic approach. Major topics include life insurance, annuities, benefit premiums, and net reserves. Students are assumed to be proficient in Multivariable calculus. A required course for Actuarial Science and Financial Mathematics majors.

Prerequisites:  STAT 280 and STAT 301

Suggested Reference:

  1. Bowers, N.L., Gerber Jr., H.U., Hickman, J.C., Jones, D.A. & Nesbit, C.J. 1997. Actuarial Mathematics (2nd ed.). Schaumburg: Society of Actuaries.
  2. Society of Actuaries Study Notes for Professional Exam M

 

STAT 482 Life Contingencies II                                                                               3-0-3

A continuation of Life Contingencies I. Development is based on a stochastic approach to life insurance models. Major topics include benefit premiums and reserves, and multi-life and multiple-decrement models. Application of such area in life insurance and property. A required course for Actuarial Science and Financial Mathematics majors. Students are assumed to be proficient in Multivariable calculus. Material in this course is based on the syllabus of Course 3 of the Casualty Actuarial Society and the Society of Actuaries.

Prerequisites:   STAT 381

Suggested Reference:

  1. Bowers, N.L., Gerber Jr., H.U., Hickman, J.C., Jones, D.A. & Nesbit, C.J. 1997. Actuarial Mathematics (2nd ed.). Schaumburg: Society of Actuaries.
  2. Society of Actuaries Study Notes for Professional Exam M

 

 

 

 

 

 

 

 

STAT 483 Actuarial Risk Theory and Credibility                                       3-0-3

This course studies the distribution of aggregate claims associated with insurance including analysis of the risk due to variations in expected claim numbers and amounts. Also covers frequency and severity distributions, individual and collective models, ruin theory, continuous-time compound Poisson surplus processes, reinsurance, dividend formulas, credibility models, and simulation. An introduction to empirical Bayes and statistical distributions used to model loss experience. Application of risk theory to the operation of insurance system and assessment of the credibility of data for ratemaking.

Prerequisites:   STAT 415 (Stochastic Process for Actuaries)

Suggested Reference:

  1. Klugman, S.A.; Panjer, H.H.; and Willmot, G.E., Loss Models: From Data to Decisions (Second Edition), 2004, John Wiley and Sons, New York
  2. Bowers, N.L., Gerber Jr., H.U., Hickman, J.C., Jones, D.A. & Nesbit, C.J. 1997. Actuarial Mathematics (2nd ed.). Schaumburg: Society of Actuaries.
  3. Beard, R.E., Pentikainan, T. & Pesonen, E. 1984. Risk Theory: The Stochastic Basis of Insurance (3rd ed.). London: Chapman & Hall.
  4. Daykin, C.D., Pentikainen, T. & Pesonen, M. 1994. Practical Risk Theory for Actuaries. London: Chapman & Hall.
  5. Herzog, T.N., Introduction to Credibility Theory (Third Edition), 1999
  6. Dean, C.G., "Topics in Credibility Theory," 2004 (SOA Study Note C-24-05).
  7. Mahler, H.C.; and Dean, C.G., "Credibility," Foundations of Casualty Actuarial Science (Fourth Edition), 2001, Casualty Actuarial Society, Chapter 8, Section 1 (background only) and Sections 2-5. (Also available as SOA Study Note C-21-01.).
  8. Society of Actuaries Study Notes for Professional Exam C

 

Some relevant learning objectives from the Society of Actuaries for:

Survival and Severity Models Range of weight: 30-35 percent

1.        Students should be able to work with discrete and continuous univariate probability distributions for failure time random variables. They will be expected to set up and solve equations in terms of life table functions, cumulative distribution functions, survival functions, probability density functions, and hazard functions (e.g., force of mortality), as appropriate. They should have similar facility with models of the joint distribution of two failure times (multiple lives) and the joint distribution of competing risks (multiple decrement).

Ruin Theory Range of weight: 3-7 percent

1.        Students should be able to analyze the probability of ruin using various models. Other topics covered in this section include determining the distribution characteristics of the amount of surplus (deficit) at the first time below the initial level as well as the impact of reinsurance. (Knowledge regarding reinsurance terminology is not assumed. Cash flows from reinsurance will be determinable based on the description of the reinsurance provided on the examination.)

Credibility

1.        Apply limited fluctuation (classical) credibility including criteria for both full and partial credibility.

2.        Perform Bayesian analysis using both discrete and continuous models.

3.        Apply Bühlmann and Bühlmann-Straub models and understand the relationship of these to the Bayesian model.

4.        Apply conjugate priors in Bayesian analysis and in particular the Poisson-gamma model.

5.        Apply empirical Bayesian methods in the nonparametric and semiparametric cases

Simulation

1.        Simulate both discrete and continuous random variables using the inversion method.

2.        Estimate the number of simulations needed to obtain an estimate with a given error and a given degree of confidence.

3.        Use simulation to determine the p-value for a hypothesis test.

4.        Use the bootstrap method to estimate the mean squared error of an estimator.

5.        Apply simulation methods within the context of actuarial models.

STAT 488 Actuarial Science Problem Labs                                                             0-1-1

This problem lab is designed to prepare Actuarial majors for the first two Society of Actuaries and Casualty Actuarial Society Examinations: Exam P (Probability) and FM (Financial Mathematics). Students are assumed to have taken the appropriate prerequisite courses prior to registering for this society exam preparation lab.

Prerequisites:   STAT 301 and MATH 131 for Exam P, or STAT 280 for Exam FM

Suggested Reference:

  1. Society of Actuaries Study Notes for Professional Exam P or FM

 

STAT 498 Topics in Actuarial Science                                                                     3-0-3

Open for Actuarial majors interested in studying an advanced topic in Actuarial Science and Financial Mathematics. Course content is variable. Possible Topics: (1) Graduation Theory, (2) Advanced Risk Theory, (3) Simulation Methods, (4) Mathematics of the Takaful System or (5) Other Advanced Actuarial Science and Financial Mathematics  topic.

Prerequisites: Senior Standing, permission of the Department Chairman upon recommendation of the instructor.

 

IAS 420 Introduction to Islamic Insurance (Takaful)                                                         3-0-3

Description to be drafted and agreed upon by IAS, Math, and Finance committee on Actuarial Science and Financial Mathematics.

Prerequisites: To be determined.

 

IAS 421 Introduction to Islamic Finance                                                                             3-0-3

Description to be drafted and agreed upon by IAS, Math, and Finance committee on Actuarial Science and Financial Mathematics.

Prerequisites: To be determined.

 


 

Existing Courses Utilized with some modification for Actuarial majors.

 

MATH 321 Introduction to Numerical Computing (for Actuaries)             3-0-3

Floating-point arithmetic and error analysis. Solution of non-linear equations. Polynomial interpolation. Numerical integration and differentiation. Data fitting. Solution of linear algebraic systems. Initial and boundary value problems of ordinary differential equations. Only one of MATH 321 or SE 301 can be taken for credit.

Prerequisites: MATH 201; ICS 101, ICS 102, or ICS 103  

 

Modification for Actuarial majors (addition of topics)

Algorithms; finite differences; interpolation; graduation; cubic splines; linear and quadratic programming; individual risk models; life tables.  Prerequisites:  multivariate calculus and linear algebra. This course section is designed to meet the Actuarial Science and Financial Mathematics  course degree requirement.

Prerequisites: MATH 201, MATH 260; ICS 101, ICS 102, or ICS 103 

 

Some relevant learning objectives from the Society of Actuaries for:

Interpolation and Smoothing

1.       Demonstrate an understanding of the purpose of smoothing (graduating) data.

2.       Apply polynomial splines, and cubic splines in particular, to actuarial data (interest rate, inflation rates, death rate, birth rate, etc over time). 

STAT 415 Stochastic Processes (for Actuaries)                                                      3-0-3

Basic classes of Stochastic processes Poisson and renewal processes with applications

in simple queuing systems. Discrete and continuous time Markov chains. Birth-Death and Yule processes. Branching models of population growth and physical processes.

Prerequisites: STAT 301

 

Modification for Actuarial majors (addition of topics)UNL &UI

Basic classes of Stochastic processes Poisson (regular, compound, compound surplus, and non-homogenous) and renewal processes with applications in simple queuing systems and actuarial science. Discrete and continuous time Markov chains. Birth-Death and Yule processes. Branching models of population growth and physical processes. Frequency and severity distibutions; individual and collective risk models; simulation. Arithmetic and geometric Brownian motions, and applications of these processes in computation of resident fees for continuing care retirement communities, and pricing of financial instruments. This course section is designed to meet the Actuarial Science and Financial Mathematics  course degree requirement.

Prerequisites: STAT 301

Suggested Reference (from Society of Actuaries) to supplement course:

  1. Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; and Nesbitt, C.J., Actuarial Mathematics (Second Edition), 1997, Society of Actuaries
  2. Daniel, J.W., "Multi-state Transition Models with Actuarial Applications," Study Note, 2004.
  3. Klugman, S.A.; Panjer, H.H.; and Willmot, G.E., Loss Models: From Data to Decisions (Second Edition), 2004, John Wiley and Sons, New York, Chapters 1-3, 4.1-4.5, 4.6.1-4.6.4, 4.6.5
  4. Ross, S.M., Introduction to Probability Models (Eighth Edition), 2003, Academic Press, San Diego
  5. Society of Actuaries Study Notes for Professional Exam M

Some relevant learning objectives from the Society of Actuaries for:

Survival and Severity Models Range of weight: 30-35 percent

1.        Students should be able to use Markov Chains in order to determine state probabilities and transition probabilities.

Frequency Models  Range of weight: 13-17 percent

1.        Students should be able to define frequency (counting) distributions, and be able to use the parameters and moments of these distributions. Students should be able to work with the families of distributions generated by algebraic manipulation and mixing of the basic distributions presented.

2.        Students should learn to solve problems using stochastic processes. They should learn how to determine the probabilities and distributions associated with these processes. Specifically, Students should be able to use a Poisson process in these applications.

Aggregate (Compound) Models Range of weight: 10-15 percent

1.        Describe properties of aggregate loss models and calculate probabilities associated with a compound distribution.

2.        Adjust the calculations for the effect of policy modifications such as deductibles, policy limits, and coinsurance.

3.        For a compound Poisson process, calculate moments associated with the value of the process at a given time

 

STAT 475 Statistical Models for Lifetime Data                                                      3-0-3

Life tables, graph and related procedures. Single samples: complete or Type II censored data and Type I censored data for Exponential, Weibull, Gamma and other Distributions. Parametric regression for Exponential, Weibull and Gamma Distributions. Distributions-free methods for proportional hazard and related regression models.

Prerequisites: STAT 302, STAT 310

 

Modification for Actuarial majors (addition of topic and some change in focus) UNL

Title: Survival Models for Actuaries

The statistical process of analyzing survival data, particularly for insurance applications. Techniques for estimating mortality rates; construction of mortality tables from the records of insured lives, employee benefit plans, and population statistics. Special attention to censoring and truncation. Life tables, graph and related procedures. Single samples: complete or Type II censored data and Type I censored data for Exponential, Weibull, Gamma and other Distributions. Parametric regression for Exponential, Weibull and Gamma Distributions. Distributions-free methods for proportional hazard and related regression models. This course section is required for Actuarial Science and Financial Mathematics  major.

Prerequisites: STAT 302, STAT 310

Suggested Reference:

  1. London, R.L. 1997. Survival Models and Their Estimation (3rd Ed.) Connecticut: ACTEX Publications
  2. Pollard, A.H., Pollard, G.N. & Yusof, F. 1981. Demographic Techniques. Oxford: Pergamon Press.
  3. Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; and Nesbitt, C.J., Actuarial Mathematics (Second Edition), 1997, Society of Actuaries
  4. Daniel, J.W., "Multi-state Transition Models with Actuarial Applications," Study Note, 2004.
  5. Klugman, S.A.; Panjer, H.H.; and Willmot, G.E., Loss Models: From Data to Decisions (Second Edition), 2004, John Wiley and Sons, New York, Chapters 1-3, 4.1-4.5, 4.6.1-4.6.4, 4.6.5
  6. Lee, Y.S., "The Mathematics of Excess of Loss Coverages and Retrospective Rating-A Graphical Approach," Section 1, PCAS LXXV, 1988, pp. 49-54.
  7. Society of Actuaries Study Notes for Professional Exam M or ACTEX Study Manual 160.

 

 

Some relevant learning objectives from the Society of Actuaries for:

Survival and Severity Models Range of weight: 30-35 percent

1.        Students should be able to work with discrete and continuous univariate probability distributions for failure time random variables. They will be expected to set up and solve equations in terms of life table functions, cumulative distribution functions, survival functions, probability density functions, and hazard functions (e.g., force of mortality), as appropriate. They should have similar facility with models of the joint distribution of two failure times (multiple lives) and the joint distribution of competing risks (multiple decrement).

2.        Students should be able to define severity distributions and be able to use the parameters and moments of these distributions. Students also should be able to work with the families of distributions generated by algebraic manipulation and mixing of the basic distributions presented.

3.        Students should be able to use Markov Chains in order to determine state probabilities and transition probabilities.

 


 

ACTUARIAL SCIENCE AND FINANCIAL MATHEMATICS  CURRICULUM

COURSE

TITLE

LT

LB

CR

 

COURSE

TITLE

LT

LB

CR

First Year (Preparatory)

 

 

 

 

 

 

 

 

 

 

ENGL

001

Preparatory English I

15

5

8

 

ENGL

002

Preparatory English II

15

5

8

MATH

001

Preparatory Math I

3

1

4

 

MATH

002

Preparatory Math II

3

1

4

PYP

001

Preparatory Physical Sciences

2

0

2

 

PYP

002

Preparatory Computer Sciences

0

2

1

PYP

003

University Study Skills

0

2

1

 

ME

003

Preparatory Engineering Technology

0

2

1

PE

001

Preparatory Physical Education I

0

2

1

 

PE

002

Prep. Physical Educ. II

0

2

1

 

 

 

20

10

16

 

 

 

 

18

12

15

Total credit hours required in Preparatory Program: 31

Second Year (Freshman)

 

 

 

 

 

 

 

 

 

 

ENGL

101

English Composition I

3

0

3

 

ENGL

102

English Composition II

3

0

3

IAS

111

Belief and its Conseq.

2

0

2

 

IAS

101

Practical Grammar

2

0

2

ICS

103

Intro to Computing

2

3

3

 

MATH

131

Finite MathematicsP, FM

3

0

3

XXX

xxx

Natural Science (CHEM 101 or PHYS 133)

3

4

4

 

MATH

102

Calculus II

4

0

4

MATH

101

Calculus I

4

0

4

 

ECON

201

Prin of Economics II (MACRO)VE

3

0

3

ECON

101

Prin of Economics I (MICRO)VE

3

0

3

 

PE

101

Physical Education I

0

2

1

 

 

 

17

7

19

 

 

 

 

15

2

16

 

 

 

 

 

 

 

 

 

 

 

 

 

Third Year (Sophomore)

 

 

 

 

 

 

 

 

 

 

ENGL

214

Technical Report Writing

3

0

3

 

IAS

211

Ethics in Islam

2

0

2

PE

102

Physical Education II

0

2

1

 

ACCT

202

Prin of Accounting II

3

0

3

ACCT

201

Prin of Accounting I

3

0

3

 

MATH

321

Intro to Numerical Computing

3

0

3

MATH

201

Calculus III

3

0

3

 

STAT

212

Business Statistics IIVS

3

0

3

MATH

260

Intro to Diff Equations & Linear Algebra

3

0

3

 

STAT

301

Intro to Probability TheoryP

3

0

3

STAT

201

Intro to StatisticsVS

2

2

3

 

 

 

 

 

 

 

 

 

 

14

4

16

 

 

 

 

14

0

14

Fourth Year (Junior)

 

 

 

 

 

 

 

 

 

 

IAS

311

Islamic Shareah

2

0

2

 

IAS

201

Objective Writing

2

0

2

FIN

301

Financial Management IVF

3

0

3

 

STAT

381

Life Contingencies IM

3

0

3

STAT

310

Regression AnalysisVS

3

0

3

 

STAT

415

Stochastic Process for ActuariesM

3

0

3

STAT

280

Financial MathematicsFM

3

0

3

 

FIN

420

InvestmentsVF

3

0

3

STAT

302

Statistical Inference

3

0

3

 

STAT

488

Actuarial Lab II

0

1

1

STAT

488

Actuarial Lab I

0

1

1

 

STAT

460

Times SeriesVS

3

0

3

 

 

 

14

1

15

 

 

 

 

14

1

15

 

 

 

 

 

 

 

STAT

399

Summer Training

0

0

2

Fifth Year (Senior)

 

 

 

 

 

 

 

 

 

 

XXX

xxx

Elective Track Course I (IAS 420 etc)

3

0

3

 

STAT

475

Survival  Models for ActuariesM

3

0

3

STAT

482

Life Contingencies IIM

3

0

3

 

IAS

301

Literary Styles

2

0

2

STAT

483

Actuarial Risk Theory and CredibilityC

3

0

3

 

STAT

xxx

Actuarial Elective III

3

0

3

XXX

xxx

Free Elective I

3

0

3

 

STAT

xxx

Actuarial Elective IV

3

0

3

STAT

xxx

Actuarial Elective II

3

0

3

 

XXX

xxx

Free Elective II

3

0

3

 

 

 

15

0

15

 

 

 

 

14

0

14

 

 

 

 

 

 

 

 

 

 

 

 

 

Total credit hours required in Degree Program: 126

Total credit hours required in General Education Hours: 62

Total credit hours required in Major Prerequisite Hours: 9

Total credit hours required in Major Requirement Hours: 35

Total credit hours required in Major Electives: 12

Total credit hours required in Other Electives: 6

VF

courses covering Finance topics for the SOA Validation by Educational Experience (VEE)

 

 

 

VE

courses covering Economics topics for the SOA Validation by Educational Experience (VEE)

 

 

 

VS

courses covering Applied Statistical Methods topics for the SOA Validation by Educational Experience (VEE)

P

courses covering topics for the SOA professional exam P (Probability)

F

courses covering topics for the SOA professional exam FM (Financial Mathematics)

 

 

 

M

courses covering topics for the SOA professional exam M (Actuarial Models)

C

courses covering topics for the SOA professional exam C (Constructing & Validating Actuarial Models)

 

Potential Contacts for Actuarial Science

 

1)       Mohammad Al Jarf

Professor of Islamic Finance

Umm Al Qura University

 

2)       Dr. S. Bin Hethlen

IAS Department
Ph.D., University of Birmingham, UK
Research Interests include: Islamic Economics
Email: hethlen@kfupm.edu.sa

 

3)       UKM faculty, Bangi, Malaysia

 

4)       UUM faculty, Sintok, Malaysia

 

5)       K-Professional Academy (KPDA) sdn bhd, Malaysia

 

6)       www.takaful.info

 

7)       Muhanna foundation, Beirut, Lebanon