The Research Committee of The Actuarial Foundation (TAF), the Casualty Actuarial Society (CAS) and the Committee on Knowledge Extension Research (CKER) of the Society of Actuaries support the advancement of knowledge in actuarial science through its support of research. Below is a list of completed research projects:
September 2010
Accepted by NAAJ
Luyang Fu and C. K. ‘Stan’ Khury, Optimal Layers for Catastrophe Reinsurance
May 2010
Accepted by NAAJ
Dr. Laura Ballotta, Efficient Pricing of Rachet Equity Indexed Annuities in a VG Economy
February 2010
Accepted by Variance
Samuel H. Cox, Yijia Lin, Ruilin Tian and Luis F. Zuluaga, Bounds for Probabilities of Extreme Events Defined by Two Random Variables
January 2010
Accepted by The Journal of the American Statistical Association
Sam Efromovich, Dimension Reduction and Adaption in Conditional Density Estimation
Accepted by NAAJ
Nariankadu D. Shyamalkumar, An Asymptopic Analysis of the Bootstrap Bias Correction for the Empirical CTE
October 2009
Accepted by NAAJ
Eric Ulm, The Effect of Policyholder Transfer Behavior on the Value of Guaranteed Minimum Death Benefits
July 2009
Accepted by NAAJ
Sheldon Lin, Ken Seng Tan, Valuation of Variable Annuities
May 2009
Vytaras Brazauskas, Robust and Efficient Fitting of Loss Models: Diagnostic Tools and Insights
March 2009
Doug Andrews, Robert L. Brown, Is Defined Contribution a Panacea for Defined Benefit Social Security Funding Problems?
Older Projects
Dimension Reduction and Oracle Optimality in Conditional Density Estimation and Actuarial Application
By Sam Efromovich, Ph.D.
Dr. Efromovich was awarded a grant by The Actuarial Foundation and the Casualty Actuarial Society to complete research on the theory, methodology and methods of multivariate conditional density estimation and its application to the analysis of credit scoring as a fair rating variable. Completed research published in the June 2010 Journal of the American Statistical Association.
Life Insurance Account
By Robert Reuter, MAAA, FSA
Robert Reuter was awarded a grant to study the components of individual life insurance and annuity plan premiums in order to provide new insights into their nature and to encourage consumer-driven programs.
Pricing Life Insurance Under Stochastic Mortality via the Instantaneous Sharpe Ratio
By Virginia Young, Ph.D., FSA
Virginia Young, University of Michigan, University of Michigan, has been awarded a grant from the AERF Committee of TAF to apply the method of Milevsky, Promislow, and Young to price life insurance.
An Empirical Examination of Jump Risks in U.S. Equity and Bond Markets
By Geoffrey Friesen, Ph.D., ASA
Geoffrey Friesen, University of Nebraska-Lincoln, has been awarded a grant from the AERF Committee of TAF, the SOA Committee on Finance Research and the SOA Investment Section Council to examine three empirical questions of direct interest to actuaries: What is the contribution of jump risk to total asset risk? Does the distribution or magnitude of jump risk vary across asset classes? Within a particular class of assets, does cross-sectional variation exist in the distribution of jump risk?
The Bootstrap Method for Calibrating Equity Models
by Dr. Mary R. Hardy, ASA, FCIA
Mary Hardy, University of Waterloo, has received a grant from The Actuarial Foundation of Canada (AFC) along with The AERF Committee of TAF to explore various aspects of bootstrap methods to provide practical solutions to important actuarial problems.
Biological and Psycho-behavioral Correlates of Risk Taking, Credit Scores, and Automobile Insurance Losses: Toward an Explication of Why Credit Scoring Works
by Patrick Brockett
This research explains “why”, from a biological and psychological perspective, the advent of the use of a person’s credit history to predict losses is one of the most important developments in the past two decades of predicting insurance losses in automobile and homeowners insurance based upon the personal characteristics of the proposed insured. It will show a distinct blood chemistry and psychological profile for financial risk takers.
Pricing of Guaranteed Annuity Conversion Options
by Laura Ballotta, Ph.D., MSc, BSc and Steven Haberman, Ph.D., MA, DSc, FIA, ASA.
This project presents a theoretical model for the pricing of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The project was published in Insurance: Mathematics and Economics, Vol. 38, Issue 1, February 2006.
Some Nonlinear Time Series Models for Actuarial Use
Wai-Sum Chan, The University of Hong Kong intends to present some advanced nonlinear time-series techniques that might be useful in building stochastic models for pricing and reserving; and to illustrate these techniques step-by-step so that actuaries or actuarial students not expert in this area can still perform the procedures.
Bayesian Reserving Methods Inspired by Chain Ladder Methods and Implemented Using WinBUGS
David Scollnik, University of Calgary, is examining the Bayesian implementation and analysis of various chain ladder models using Markov Chain Monte Carlo simulation methods via WinBUGS. The finished paper can be found in ARCH 2004.2.
Distance Education for Actuarial Students
by Robert L. Brown, Unviversity of Waterloo
Two non-credit distance learning education courses have been created for use by SOA/CAS actuarial students.
In the first course, Interest Theory and Finance, Professor Brown explores aspects of the Kellison textbook, The Theory of Interest as it applies to the SOA/CAS Course 2. The second course, Introduction to Ratemaking and Loss Preserving for Property and Casualty Insurance provides modules on automobile and homeowners insurance, worker's compensation, liability insurance, changing risk classifications and many others.
Calculating Insurance Premiums Using Dependent Risk Models and Catastrophe Databases
by Dr. Thierry Duchesne, ASA, Dr. Etienne Marceau, ASA and Dr. Helene Cossette
The researchers have derived systematic methods for calculating insurance premiums when natural disasters induce dependence in the risks. Their findings are published in the October 2003 NAAJ as "Modeling Catastrophes and their Impact on Insurance Portfolios."
Stock Return Models for Financial Guarantees with Applications to Investment Guarantees in Insurance Products
by Dr. Mary R. Hardy, ASA, FCIA
An educational text, Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, was written to assist actuaries with risk management of investment guarantees. The book was published by Wiley and a description is available.
Premium Death Spirals: Theory and Empirical Evidence
by Harry Sutton, FSA, FCA, MAAA, Dr. Roger Feldman, and Dr. Bryan Dowd
The project addresses the question, do high and low health risk consumers have different preferences for premiums and benefits?
The SOA Health Section also contributed to this project.
Asset-Liability Integration
by Dr. Krzysztof Ostaszewski, FSA, CFA, MAAA
This monograph "Asset-Liability Integration" analyzes the asset-liability management process in the financial intermediation industry and conjointly strives to define a mission for the modern insurance industry, the role of the asset-liability management and its place within the financial intermediation network. This monograph was published by the Society of Actuaries. This project was jointly funded by AERF and the Casualty Actuarial Society.
Retrospective and Prospective Analysis of the Privatized Mandatory Pension System in Mexico
by Dr. Tapen Sinha
This monograph "Retrospective and Prospective Analysis of the Privatized Mandatory Pension System in Mexico" provides the backdrop of the Mexican economy and traces the history of social security and pensions in Mexico accompanied by in-depth details of both the old and new systems. It takes a deep look at fund management by privately managed funds and discusses why private management of pensions is not like privatization of other spheres of activities.
Robust and Efficient Methods for Estimation of Reinusrance Parameters
by Vytaras Brazuaskas
The purpose is to compare empirical nonparametric and robust parametric estimators of different reinsurance premiums on the basis of two criteria, efficiency and robustness. The final paper has been published in Insurance: Mathematics & Economics, Volume 32, Issue 1, February 2003.
Measurement of Relative Equity and Yaari's Theory of Risk
by Dr. Virginia Young, FSA and Dr. S. David Promislow, FCIA, FSA
Using Yaari's dual theory of risk to measure the relative inequity that arises when insurers use imperfect information to estimate the net premium of insureds. The paper, "Measurement of Relative Inequity and Yaari's Dual Theory of Risk" was published in Insurance: Mathematics and Economics, Volume 30, Issue 1, February 2002. Another paper titled, "Decomposition Properties of Dual Choice Functionals" was published in Social Choice and Welfare, (2003), 20.
The Risk Premium Project Phase I and II Report
This report summarizes the authors' review of the actuarial and finance literature on the subject of risk adjustments for discounting liabilities in property-liability insurance. This project was also funded by the Casualty Actuarial Society.
Academic Investigators
J. David Cummins, Ph.D., University of Pennsylvania
Richard D. Phillips, Ph.D., Georgia State Universitiy
Industry Investigators
Robert P. Butsic, MBA, ASA, MAAA, Fireman's Fund Insurance Company
Richard A. Derrig, Ph.D., Automobile Insurers Bureau of Massachusetts
Sequential Quasi-Linear Credibility
by Dr. Zinoviy Landsman and Udi Makov
Completed in 2000 this research project extended the sequential approach to a problem of credibility evaluation.
Parametric and Non-Parametric Bootstrap in Actuarial Practice
by Dr. Krzysztof Ostaszewski, FSA, MAAA and Dr. Grzegorz Rempala
The goal of this project was to analyze the applications of bootstrap to actuarial science.
Actuarial Considerations Regarding Risk and Return in Property-Casualty Insurance Pricing
The Casualty Actuarial Society has published this book edited by Oakley Van Slyke. The book was first conceptualized by the CAS Valuation and Financial Analysis Committee. Actuarial Considerations was produced by the CAS with the contribution of a generous grant from the Actuarial Education and Research Fund.
Simulation Based Investigation of Optimal Funding for Defined-Benefit Schemes
by Dr. Steven Haberman ASA, FIA, Dr. Iqbal Owadally
The researchers investigated the effect of varying investment returns and inflation on defined-benefit plans. "Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans" , NAAJ, January 2004, updates the presentation, "Efficient Amortization of Actuarial Gains and Losses in Pension Plans" from the 34th Actuarial Research Conference.
Actuarial Modeling with MCMC and BUGS
by Dr. David Scollnik, ASA
The goal of this project was to examine and illustrate the use of MCMC and BUGS in a variety of actuarial modeling contexts.
Robust and Efficient Estimation of the Tail Index of a One-Parameter Pareto
by Robert Serfling and Vytaras Brazauskas
Introduces modern concepts of robust estimation into actuarial science and tries to develop improved estimators. The Casualty Actuarial Society and the Society of Actuaries Committee on Knowledge Extension Research also provided financial support.
Gain and Loss Characteristics of Average Fair Market Value Asset Valuation Methods
by Gary Bayer, EA, FSA, MAAA
The researcher explored the impact of using an average fair market value on a pension plan's gains and losses.
Approximations for Aggregate Claims and Ruin Probabilities
by Dr. Gordon Willmot, FCIA, FSA and Dr. X. Sheldon Lin, ASA
Investigated the effect of varying investment returns and inflation on defined-benefit pension plans. The final report, "Lundberg Approximations for Compound Distributions with Insurance Applications" was published in Springer's Lecture Notes in Statistics, Volume 156.
Ethics, Economics and Actuarial Considerations of Genetic Testing
by Dr. Patrick Brockett
The purpose of this project was to address the ethical and moral issues posed by the new information explosion. AERF oversaw the project that was funded entirely from the SOA Product Development Section. The final research, "Genetic Testing, Insurance Economics, and Societal Responsibility" was published in the North American Actuarial Journal, Volume 3, No. 1, January 1999.
Credibility and Equity
by Dr. Virginia Young, FSA and Dr. S. David Promislow, FCIA, FSA
To investigate the relationship between credibility and equity and answer such questions as, "How does an actuary, faced with unknown risks, use claim data to arrive at the most equitable premiums?" The SOA Committee on Knowledge Extension Research and the CAS both contributed to this project. Published in the Scandinavian Actuarial Journal, Volume 2000, Number 2/September 1, 2000.
Explaining US GAAP Reports in Mutual Life Insurance Companies
by Daniel Case, FSA
The report explains the unusual nature, in SEC filings and policyholder communications, US GAAP reports by mutual life insurers.
Insurance Pricing: Theory and Applications, and Insurance Ratemaking: Risk and Reward
by Dr. Shaun Wang, ASA
With grants from the Casualty Actuarial Society and the SOA Committee on Knowledge Extension Research, the researcher produced several papers developing pricing theory for group insurance which quantified the systematic risk associated with risk portfolio. "Premium Calculation by Transforming the Layer Premium Density" can be found in the Astin Bulletin, Volume 26, No. 1, 1996. Insurance: Mathematics and Economics published "Ordering of Risks under PH-Transforms," No. 18, 1996, and "Axiomatic Characterization of Insurance Prices," appears in ARCH 1997, Vol. 16.
The Profit Provision in the Ratemaking Formula
by Dr. Stephen D'Arcy, FCAS, MAAA and Michael Dyer
Funded by the Casualty Actuarial Society the resulting paper, "Ratemaking: A Financial Economics Approach" provides an introduction to the target total rate of return approach, the capital asset pricing model, the discounted cash flow technique, and the option pricing model, all in an insurance contract.
Bounds on Prices of Insurance Contracts and Complex Options
by Dr. Phelim Boyle, FCIA and Dr. X. Sheldon Lin, ASA
With grants from AERF and Casualty Actuarial Society the researchers studied the upper and lower bounds on the prices of two kinds of insurance contracts and options: (1) insurance contracts and options whose payoffs involved two or more random variables and (2) insurance contracts and options whose payoffs are compound distributed. Their final paper was published in the Journal of Financial Economics, Volume 46, Issue 3, December 1997.
Actuarial Gains and Losses: A Martingale Approach
by Dr. Daniel Dufresne, FSA
The researcher shows how martingale theory is used to better understand actuarial gains and losses (AGL), by deriving Decomposition Theorem for actuarial surpluses and studying the cumulative sum behavior of AGLs, with or without interest, and what their practical applications are. The results were presented in "A Decomposition of Actuarial Surplus and Applications."
Interest and Mortality Randomness: Solvency Considerations
by Dr. Gary Parker
The project attempts to determine appropriate reserves for a portfolio of insurance contracts looking at morality and investment risks. The end product was "Stochastic Analysis of an Insurance Portfolio, " presented at the 4th AFIR International Colloquium in Orlando, FL, April, 1994. It appears in AFIR, 1994, Vol. 1.
An Alternative Look at Returns of High-Yield Securities and at Risk Classification
by Dr. Krzysztof Ostaszewski, FSA, CFA, MAAA
This paper, presented at the 4th AFIR International Colloquium in Orlando, FL, April 1994, continues a line of research of applications of fuzzy set theory to property casualty and life insurance by providing an overview of fuzzy pattern recognition techniques. The paper is published in AFIR, 1994, Vol. 1.
Fluctuations of Pension Fund Contributions and Fund Levels
by Dr. Daniel Dufresne, ASA
The finished project titled, "Some Aspects of SFAS No. 87" was published in ARCH, 1993, Volume 2.
A Monte-Carlo Approach to the Analysis of Nonlinear and Non-Gaussian Actuarial Time Series
by Dr. Bradley Carlin
The paper, "State Space Modeling of Non-Standard Actuarial Time Series" gives a brief review of new methodology using non-linear and non-Gaussian scenarios when using Monte Carlo integration techniques for simple recursive updating formulae provided by the Kalman filter algorithm. This paper was published in Insurance: Mathematics and Economics, Volume 11, Issue 3, October 1992.
Educational Software for Actuarial Mathematics and Demography
by Dr. Eric Seah, FSA
"ABC of Life Contingencies" is a system of APL programs that help actuarial students study the elementary life contingencies. The programs should also help academics and practitioners in calculating actuarial values.
Information Theoretic Approach to Actuarial Science: A Unification and Extension of Relevant Theory and Applications
by Dr. Patrick Brockett
This David Garrick Halmstad award winning paper presents a unifying non-Bayesian statistical method for incorporating prior information into the determination or probability distributions (and other finite measures.)
An Introduction to the Competitive Market Equilibrium Risk Load Formula
by Dr. Glenn Meyers, FCAS, MAAA
This paper describes one of the newer premium calculation principles called the Competitive Market Equilibrium (CME) risk load formula.
Corporate Book Reserving for Postretirement Health Care Benefits
edited by Dwight K. Bartlett, FSA, MAAA
Jointly funded with the Pension Research Council, this book is a compilation of papers that were presented at a symposium at the University of Pennsylvania, 1989, dealing with balance sheet reserving for future medical cost obligations for employers. The book was published for the Pension Research Council, Wharton School, University of Pennsylvania by Irwin Publishers, 1991.
Risky Business-An Education Software for Risk Theory
by Professor Francois Dufresne and Professor Hans U Gerber, ASA
In the early 1990s, the researchers developed a software program to make the teaching and learning of risk theory more attractive.
A Stochastic Approach to Workers Compensation Pension Reserves
by Dr. Glenn Meyers, FCAS, MAAA
The researcher explores the explicit calculation of a risk load for discounted loss reserves.
Projections of Active Life Expectancies and Their Applications to Long-Term Care Coverages
by Dr. John Beekman, ASA, MAAA
The paper, "An Alternative Premium Calculation Method for Certain Long-Term Care Coverages" refines projections of active life expectancies and improves probability models for long-term care coverages. Also, one model is used to provide an alternative premium calculation method. This paper was published in ARCH, 1990, Volume 2.
Textbook on Mathematics of Investment and Credit
by Dr. Samuel Broverman, ASA
The textbook provides a thorough treatment of the mathematics of investment and credit incorporating theory and applications. A second edition (1996) is available from any of the SOA book distributor.
Modeling Life and Health Insurance Operations with Solvency Considerations
by Dr. Edward (Jed) Frees, FSA
The project funded by AERF and the Society of Actuaries proposed a generalized framework for quantifying the relative importance of sources of risk so that risk managers would be better to understand risk factors and their effect on financial security systems. The research resulted in several papers, including one coauthored with Dr. Siu Wai Lai, "Examining Changes in Reserves using Stochastic Interest Rate Models," published in the Journal of Risk and Insurance, September 1995, Volume 62, No. 3, and another paper, "Relative Importance of Risk Sources in Insurance Systems," that appeared the North American Actuarial Journal, Volume 2, No. 2, 1998.
Mathematical Models for Active Life Expectancy
by Dr. John A. Beekman, ASA, MAAA
The paper, "Active Life Expectancies and their Actuarial Uses," presents synopses of many papers that could prove helpful to actuaries and others for looking at the insurance needs for long-term health care for the elderly. In the paper are mathematical expressions for active life expectancies, projections of active life expectancies, through the 2040, and some material on the estimation of long-term health care costs.
Insurance Risk Models
by Dr. Harry H. Panjer, FCIA, FSA, and Dr. Gordon E. Willmot, FCIA, FSA
The book discusses the distribution of aggregate claims for an insurer that can be computed by simple recursive algorithms for a very wide range of claim number models with any loss distribution. This book is out of print but a hard copy is available in the SOA library.
Measuring The Interest Rate Risk
by Paul R. Milgrom
Beginning with which asset values are economically relevant and at risk the paper develops the theory of measurement of interest rate risks from its foundations.
Bayesian Credibility
By Dr. Stuart Klugman, FSA
In "Credibility for Classification Ratemaking via the Hierarchical Normal Linear Model" the author develops a true Bayesian approach to the classification ratemaking credibility problem. . Using a true Bayesian analysis with a hierarchical normal linear model, the paper, "Bayesian Credibility Under Parameter Uncertainty" shows that variances can be estimated and the credibility factors determined.
Actuarial Projections for the Old-Age, Survivors, and Disability Insurance Program of Social Security in the United States of America
by Dr. George H. Andrews, ASA and Dr. John A. Beekman, ASA
This monograph discusses Social Security, primarily the Old-Age, Survivors, and Disability Program (OASDI), which provides benefits to workers, spouses and survivors whose incomes have been affected by old-age, death, and disability. Contributions from 24 insurance companies and 15 consulting firms helped finance this project. This book is available from the SOA bookstore for $25.00
Fine Tuning a Whittaker-Henderson Graduation
by Dr. James D. Broffit, ASA
"Refinements of Whittaker Graduation through the Minimization of Bayes Risk" discusses the accuracy of a graduation process measured by Bayes risk.
An Analysis of the Capital Structure of an Insurance Company
by Dr. Glenn Meyers, FCAS, MAAA
The paper analyzes the capital structure of an insurance company and develops a model that analyzes the effect of uncertainty in the loss reserves, the underwriting cycle and the cost of insurance regulation to the consumer.
Survival Models and Their Estimation
by Richard London, FSA
A general textbook describing the properties and characteristics of survival models and statistical procedures for estimating such models from sample data. A new edition of the text can be ordered from ACTEX Publications.
On Applications of Finance Theory to Property-Liability Insurance Pricing
by Dr. Stephen D'Arcy, FCAS, MAAA and Dr. Neil A. Doherty
The project resulted in a single source that explains to actuaries, regulators and insurance academics the basic financial theories and techniques applicable to property-liability insurance pricing. The work was published as Monograph No. 15, The Financial Theory of Pricing Property Liability Insurance Contracts, by S.S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania.
Operations Research Applications in Actuarial Science and Insurance
by Dr. Arnold Shapiro, EA, FSA, MAAA, MSPA
The paper provides an overview of literature reviewed as a study of applications of operations-research techniques in insurance.
Employer Accounting for Pensions: An Analysis of the Financial Accounting Standards Board's Preliminary Views and Exposure Draft
by E.L. Hicks, CPA and C.L. Trowbridge, FSA, MAAA
The monograph attempts to explain "Preliminary Views on Major Issues Related to Employer Accounting for Pensions and Other Postemployment Benefits" (PV), a document released by the FASB in November 1982, to employers, and other interested professionals some of the reasons why the proposals have not been accepted. The research was also sponsored by the Pension Research Council of the Wharton School and was published in 1985 by Richard D. Irwin, Inc., Homewood, IL.
Empirical Bayesian Credibility for Workers' Compensation Classification Ratemaking
by Dr. Glenn Meyers, FCAS, MAAA
The paper demonstrates, using an empirical Bayesian credibility formula, how a company can derive accurate classification relativities.
Loss Distributions
by Robert V. Hogg and Dr. Stuart A. Klugman, FSA
This book deals with the problem of fitting probability distribution models to data. Several companies along with the American Academy of Actuaries and the Casualty Actuarial Society made contributions to AERF for preparation of the book. It was published by John Wiley & Sons in 1984.
Fundamental Concepts of Actuarial Science
Charles L. Trowbridge, F.S.A., M.A.A.A.., E.A. - (Revised Edition)
The Actuarial Education and Research Fund (AERF) lent its support to many of the projects that occured before 2004.
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