Committee on Knowledge Extension Research [CKER]

This section contains the results of research projects and studies that were funded by the Committee on Knowledge Extension Research (CKER). Projects are selected through an open topic annual grant competition. These studies tend to be more theoretical in nature and have application to many different practice areas. Projects usually conclude with publication in a peer reviewed journal. We encourage you to browse throughout these diverse topics.


Aging & Post-Retirement

  • Public Employees Retirement Systems
    Michael Samet, EA, FCA, FSA, MAAA, Timothy Peach, EA, FSA, MAAAand W. Paul Zorn
    The monograph published by the Society of Actuaries is the first comprehensive study and review of actuarial methods used by public employees retirement systems (PERS).
  • Investing for Retirement: Optimal Capital Growth and Dynamic Asset Allocation (1999)
    Hans U. Gerber, ASA, Ph.D. and Elias S. Shiu, ASA, Ph.D.
    Published in the April 2000 NAAJ.


General Insurance

  • Factor Copula Approaches for Assessing Spatially Dependent High-Dimensional Risks
    Lei Hua, Ph.D, ASA; Michelle Xia, Ph.D; and Sanjib Basu, Ph.D.
    The researchers proposed an innovative approach for modeling spatial dependence among losses from various geographical locations.
  • Estimating the Probability of a Rare Event via Elliptical Copulas
    Liang Peng, Ph.D.
    The researcher modeled and predicted multi-dimensional rare events by combining volatility models and tail copulas.
  • Robust and Efficient Methods for Credibility  
    Vytaras Brazauskas, Ph.D.
    The researcher developed an ensemble of improved data-analysis procedures, which offer various trade-offs between robustness and efficiency. Practical guidelines regarding the choice of appropriate robustness-efficiency trade-off in applications were established.
  • Toward a Unified Approach to Fitting Loss Models  
    Stuart Klugman, Ph.D., FSA and Jacques Rioux, Ph.D., ASA
    The researchers extended the results of Clive Keatinge's paper," Modeling Losses with the Mixed Exponential Distribution". The paper is published in the North American Actuarial Journal, January 2006, Vol. 10, Issue 1.
  • Credibility Using Copulas
    Edward(Jed) Frees, FSA, MAAA, Ph.D. and Ping Wang, Ph.D.
    The researchers developed a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes. The paper was published in the April 2005 NAAJ.
  • Contaminated Expotential Dispersion Loss Models
    Professor Udi E. Makov and Professor Zinoviy Landsman
    The research develops families of contaminated exponential dispersion loss models and examined their theoretical properties and applicability to real heavy tailed loss data. It was published in the April 2003 NAAJ.
  • Robust and Efficient Fitting of Loss Models  
    Dr. Robert Serfling
    The researcher developed estimators which are both efficient and robust. The results are published in the October 2002 NAAJ.
  • Credibility and Equity
    Dr. Virginia Young, FSA and Dr. S. David Promislow, FCIA,FSA
    Investigated the relationship between credibility and equity and answered such questions as, "How does an actuary, faced with unkown risks, use claim data to arrive at the most equitable premiums?" The paper was published in the Scandinavian Actuarial Journal, Volume 2000, Number 2/September 2000.
  • Pricing Decisions in Insurance: A Fuzzy Logic Approach
    Dr. Virginia Young, FSA
    The project researches how an actuary can use fuzzy logic to make pricing decisions that consistently consider supplementary data. Dr. Young's results can be found in the following two papers:" Adjusting Indicated Insurance Rates: Fuzzy Rulesthat Consider Both Experience and Auxiliary Data ," Proceedings, Volume LXXXIV, 1997, Casualty Actuarial Society and " Insurance Rate Changing: A Fuzzy Logic Approach,"Journal of Risk and Insurance, September 1996, Volume 63, Number3.
  • A Longitudinal Data Analysis Interpretation of Credibility Models (1998)
    Edward A. Frees, FSA, Ph.D., Yu Luo, ASA and Virginia R. Young,FSA, Ph.D.
    Published in Insurance: Mathematics and Economics, Volume 24,Issue 3 (28, May 1999)


  • Capital Allocation using the Bootstrap
    Joseph H.T. Kim, Ph.D, FSA, CERA
    The researcher reviewed parametric dependency modeling (or copula fitting) with a small-sized multivariate sample.
  • Portfolio Optimization under Solvency Constraints: A Dynamical Approach
    Sujith Asanga, Alexandru Asimit, Ph.D; Alexandru Badescu, Ph.D; Steven Haberman, Ph.D.
    The researchers developed portfolio optimization problems for a non life insurance company seeking to find the minimum capital required that simultaneously satisfies solvency and portfolio performance constraints. 
  • Canadian Retirement Incomes: How Much Do Financial Market Returns Matter? 
    Lars Osberg, Bonnie-Jeanne MacDonald, FSA
    The researchers compared three scenarios to determine how poor financial market returns may affect the financial well-being of Canadian seniors.
  • Incorporating Spatial Dependence and Climate Change Trends for Measuring Long-Term Temperature Derivative Risk
    Robert Erhardt, ACAS
    The researcher explored a method to model the financial risks of holding portfolios of long-term temperature derivatives for any subset of the 30 North American cities whose derivatives are actively traded on the Chicago Mercantile Exchange.
  • Move-Based Hedging of Variable Annuities: A Semi-Analytic Approach 
    X. Sheldon Lin, Ph.D;  Panpan Wu; and Xiao Wang, Ph.D.
    The researchers proposed a semi-analytic algorithm for measuring the mean and variance of the cost associated with a two-sided move-based hedging of options written on an underlying asset whose price follows a geometric Brownian motion. 
  • Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application
    Jun Cai, Ph.D; David Landriault, Ph.D, FSA, FCIA; Tianxiang Shi, Ph.D; and Wei Wei, Ph.D.
    The researchers studied joint-ruin problems of two risk undertakers in a proportionally shared Markovian claim arrival process.
  • Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model
    Zhenyu Cui, Ph.D; Runhuan Feng, Ph.D; and Anne MacKay, Ph.D.
    The researchers put forth a theoretical basis with a parametric model to analyze the impact of the VIX-linked fee structure and to verify some claims from the Chicago Board of Options Exchange.
  • On A Generalization of the Gerber-Shiu Function
    Manuel Morales, Ph.D. and Enrico Biffis, Ph.D.
    The researchers proposed an extended definition of the expected discounted penalty function that takes into account two new random variables: the surplus at last minimum before ruin and the time since this last minimum.
  • Weighted Premium Calculation Principles and Risk Capital Allocations
    Ricardas Zitikis, Ph.D.
    The researcher "reintroduced" the concept of univariate and multivariate weighted distributions, emphasizing their potential applications and usefulness in the actuarial context and developed a general class of premium calculation principles.
  • Underwriting Cycle and Ruin Probability
    Bruce Jones, Ph.D, FSA, FCIA
    The researcher developed a model for the surplus process that appropriately reflects pricing cycles; he explored the sensitivity of ruin probabilities to changes in characteristics of pricing cycles, and investigated the impact on the surplus process of two strategies for responding to pricing cycles.
  • Estimating the Actuarial Cost Function of Financial Distress
    Shaun Wang, Ph.D., ASA, FCAS and Andreas Milidonis,Ph.D.
    The researchers derived an analytical framework and performed empirical estimations of the actuarial cost function of financial distress, expressed as a function of the distance-to-default.
  • The Distribution of the Sum of Lognormals
    Daniel Dufresne, Ph.D., FSA
    The researcher priced lognormals with a particular emphasis on the numerical application of the theoretical results to the pricing of Asian and basket options. The project resulted in two papers:
  • Mathematical Models and Software for Financial Organizations at Risky Markets
    Vladimir Morozov, Ph.D. and Alexander Vasin, Ph.D.
    The researchers developed mathematical methods and software for accumulation of the capital and investment portfolio management problems under specific conditions of the Russian financial markets. The paper was accepted for publication by the International Journal of Mathematics, Game Theory and Algebra.
  • Application of Quasi-Monte Carlo Methods to Actuarial Science
    Phelim Boyle, FCIA, Ph.D. and Ken SengTan, ASA, Ph.D.
    The project resulted in two research publications:
  • The Inner Workings of Neural Networks and Genetic Algorithms  
  • Generalized Cox, Ingersoll and Ross Model: Statistics and Valuation of Interest Rate Derivatives
    Dr. Wojciech Szatazchneider
    Dr. Szatazchneider presents a simple construction of the extended Cox, Ingersoll and Ross model for term structure of interest rate, and a simple way of pricing general interest rate derivatives with this model. The paper was published in the Mexican Journal of Economics and Finance, Volume 1, Number 4, 2002.
  • The Cost of Mismatch in Stochastic Interest Rate Models  
    Dr. Michel Jacques, ASA
    Evaluated the cost of mismatch by a percentile of the cash flow distribution when interest rates follow a stochastic model.
  • Tight Approximation of Basic Characteristics of Classical and Non-classical Surplus Processes
    Vladimir Kalashnikov and Gurami Tsitsiashvili
    The paper proposes asymptotically correct two-sided bounds for random sums (where the number of summands has an arbitrary distribution) which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The paper was published in ARCH, Volume 2000.1
  • Bounding and Asymptotic Behavior of Ruin Probabilities in Collective Risk Theory
    Dr. Vladimir Kalashnikov
  • A Stochastic Model of the Asset Liability Management
    Dr. Lijia Guo, ASA
    The research addresses the stochastic modeling for managing the asset liability process. The paper was published in ARCH, 1996.1
  • Study of Public Financial Guarantee Programs   
    The monograph by Price Waterhouse LLP for the Society of Actuaries presents the results of a study of Public Financial Guarantee Programs in the United States and Canada.


Life, Mortality, & Longevity

  • Applications of Mortality Durations and Convexities in Natural Hedges
    Tzuling Lin and Cary Chi-Liang Tsai, ASA
    The researchers developed innovative methods of hedging longevity/mortality risks to facilitate the self-management of internal risks by the life insurance industry.
  • Impact of Flexible Periodic Premiums on Variable Annuity Guarantees 
    Carole Bernard, Ph.D; Zhenyu Cui, Ph.D; and Steven Vanduffel, Ph.D.
    The researchers studied the fair fee of a flexible premium variable annuity, in which the policyholder can choose to pay periodic premiums during the accumulation phase instead of a single initial premium. 
  • Pricing Funeral (Burial) Insurance in a Microinsurance World with Emphasis on Africa
    Colin Ramsay, ASA, MAAA and Luis Arcila
    The researchers provided a formal economic-actuarial analysis of a practical approach to micro-insurance.
  • Life Insurance Purchasing to Maximize Utility of Household Consumption
    Erhan Bayraktar, Ph.D. and Virginia Young, FSA
    The researchers determined the optimal strategy for purchasing life insurance under two criteria.
  • A Nonparametric Visual Test of Mixed Hazard Models
    Jaap Spreeuw, Ph.D, AAG, FIA; Jens Perch Nielsen and Søren Fiig Jarner
    The researchers identified mortality trends and produced mortality projections with the baseline mortality in accordance with the SAINT model and alternate frailty models.
  • Mortality Regimes & Pricing
    Andreas Milidonis, Ph.D, Samuel Cox, Ph.D, FSA, CERA and Yijia Lin, Ph.D.
    The researchers employed regime switching models in two areas of mortality risk and improved the modeling of the time-series common factor that affects all age cohorts as captured by Lee and Carter.
  • Optimal Surrender Strategies and Product Design for Equity-Indexed Annuities
    Kristen Moore, Ph.D, ASA
    The researcher attempted to understand optimal equity-indexed annuity policyholder behavior and product design.
  • The Optimal Allocation of Aggregate Mortality Risk
    Anthony Webb
    The researcher proposed a study of the aggregate mortality risk faced by annuity insurers.
  • Markov Mortality Models and Their Applications in Actuarial Science
    Sheldon Lin, Ph.D., A.S.A. and Xiaoming Liu
    The researchers describe the relationship between mortality and physiological variables by using finite-state Markov processes with one absorbing state to model an underlying dynamic aging process.
  • Analysis of Mortality Data Using Smooth Spline Poisson Regression
    N.D. Shyamal Kumar, Ph.D., M.Stat and Manuel Mendoza,Ph.D.
    The researchers survey Bayesian models for mortality data and related frequentist models. The paper is published in ARCH 2006.1.
  • Pricing of Guaranteed Annuity Conversion Options
    Steven Haberman, FIA, ASA
    The researcher presents a theoretical model (consistent with financial economics theory) for the pricing of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The paper will be published in Insurance: Mathematics and Economics, Vol. 38.
  • Real Longevity Insurance with aDeductible: An Introduction to Advanced-Life DelayedAnnuities  
    Moshe Milevsky, Ph.D.
    The researcher developed a better understanding of the economic pricing, efficiency and long-term evolution of the Canadian life annuity market, employing the modeling paradigm of continuous-time finance theory. The paper is published in the October 2005 NAAJ.
  • Actuarial Aspects of Dependencies in Insurance Portfolios
    Dr. J. Dhaene, Dr. M. Denurt, Dr. M. Goovaerts, R. Kaas and D.Vyncke
    The researchers studied the consequences of the introduction of dependency relations in actuarial models considering the problem at the portfolio level and the individual risk level. The following two papers were published in Insurance: Mathematics and Economics: The Concept of Comonotonicity in Actuarial Science and Finance:Theory, Volume 31, Issue 1, August 2002 , and The Concept of Conomotonicity in Actuarial Science and Finance:Applications, Volume 31, Issue 2, October 2002.
  • Pricing Practices for Joint Last Survivor Insurance
    Dr. Heekyung Youn
    Based on a Hougaard copula function and using data from a large insurance company constructed a parametric model for joint survival function. The paper was published in ARCH, Volume 2001.1.
  • Credibility Using a Loss Function From Spline Theory: Practical Considerations
    Dr. Virginia Young, FSA
    Reviews and expands previous research by developing ways to use results to calculate expected claims. The paper was published in the January 1998 NAAJ.
  • The 1996 Accidental Death Mortality Table: A Comprehensive Analysis of Recent Accidental Death Experience
    Jay Jaffe, FCIA, FSA, MAAA
    The researcher considers recent death mortality experience applicable to both life policies and other accident products and presents a possible new valuation accident death benefit mortality table of US business. The information appears in the SOA's 1997-98 TSA Reports.
  • Random Mortality Rates and the Analysis of Selective Lapsation  
    Dr. Bruce Jones, FCIA, FSA
    Studies models involving random mortality rates and assesses their suitability in analyzing insured life mortality and to develop ideas for modeling relationships between mortality rates and lapse rates. The paper was published in the January 1998 NAAJ.
  • Statistical Methods of Combining Multiple Sets of Count Data
    Dr. H. Dennis Tolley, ASA and Dr. Gilbert Fellingham
    The purpose was to examine statisical methods of estimating lapsation rates as they apply to guaranteed issue health insurance policies. One of the resulting papers, published in the July 1999 NAAJ, Combining Life Table Data, uses maximum likelihood methods to illustrate a method for combining tables of count data. Another paper published in the Scandinavian Actuarial Journal, Volume 2000, Number 2, September 2000, Likelihood Methods for Combining Tables of Data presents similar data by presenting likelihood methods of combining tables of data from several sources.

Long-Term Care

  • Development of Educational Material Related toActuarial Modeling (2000)
    Bruce Jones, FSA, Ph.D.
    The completed project, "Modeling Policyholder Outcomes under a Disability Income-Type Long-Term Care Insurance Policy," was an extension of An Introduction to Actuarial Models and Modeling: An Interactive Approach (IAMM) and has been incorporated on the SOA Course 7 syllabus.


  • Is the Cost Method of the Canada Pension Plan Suitable for Adoption by Other Countries?
    Doug Andrews, FSA, FCIA, FIA, CFA
    The researcher reviewed relevant literature, developed actuarial principles for a sound funding method of a partially funded SSRS and specified an approach for determining if a funding method is sound.
  • The Effect of Pillar 1 on Efficient Investment Portfolio Choice in the Case of the United States
    Krzysztof Ostaszewski, MAAA, FSA, CERA
    The researcher considered the U.S. Social Security system as a part of capital markets, by asking how a person’s optimal investment portfolio is affected by the existence of the Social Security System.
  • Asset-Liability Management for Pension Funds in a Time-Varying Volatility Environment
    Spyridon Vrontos, Ph.D; Ioannis Vrontos, Ph.D. and Loukia Meligkotsidou, Ph.D.
    The researchers addressed the issue of time-varying variances and co-variances of pension fund returns and gave focus on their potential impacts to pension fund portfolio construction and risk measurement.
  • Mortality Improvement Cohorts and the Effect on the Annuities Market and Social Security System in the United States
    Krzysztof Ostaszewski, Ph.D., M.S., MAAA, FSA
    In response to mortality improvement, the researcher studied special cohorts and correlations among them in various countries and their effect on prices of retirement instruments.
  • Transferring the Financial Risks of Retirement
    William Leslie, FSA, MAAA
    The researcher developed an educational model that conveys therisks and rewards of various strategies concerning assetperformance and longevity. The project resulted in a Beta version of the Retirement Income Calculator software.
  • Valuation of Equity-Indexed Annuities under Stochastic Interest Rates
    X. Sheldon Lin, ASA and Dr. Ken Seng Tan, ASA
    This paper considers the pricing of equity-indexed annuities.It was published in the October 2003 NAAJ.
  • Modern Modeling Technologies for Pension Actuaries
    Dr. Arnold F. Shaprio, EA, FSA, MAAA, MSPA
    Several articles published in ARCH were a result of the research which investigated the role of modern modeling technologies for the pension actuary.
  • Is Social Security a Regressive System?
    Dr. Robert L. Brown, ACAS, FCIA, FSA
    This paper analyzes both the Old-Age, Survivors, and Disability Insurance (OASDI) system of the US and Canada/Quebec Pension Plans(C/QPP) to determine whether these systems are "a good deal" and whether they are regressive or progressive. The paper was published in the October 1998 NAAJ.
  • The Analysis of CCRC Data
    Dr. Bruce Jones, FCIA, FSA
    Because continuing care retirement communities (CCRC) pose an interesting challenge to actuaries the researcher presents an approach to analyzing CCRC data and demonstrates the methodology by using data from a CCRC. The paper was published in the October 1997 NAAJ.
  • Methodology to Deal with Dependencies on Multi-Life Risks
    Dr. Edward (Jed) Frees, FSA, Dr. Jacques Carriere, ASA and Dr.Emiliano Valdez, FSA
    By discussing a broad class of parametric models using a copula the paper, Annuity Valuation with Dependent Mortality, which was published in ARCH, 1995.1, investigates the use of models of dependent mortality for determining annuity values.
  • The Management of De-Accumulation Risks in a Defined-Contribution Environment (2002)
    Russell Gerrard, Ph.D., Steven Haberman, FIA, Ph.D., and ElenaVigna, Ph.D.
    To provide a tool for finding the optimal investment and/orconsumption choices in defined-contribution pension schemes in the decumulation phase, when the income drawdown option is taken by the pensioner. The paper was published in the North American Actuarial Journal, January 2006, Volume 10, No. 1.
  • Forecasting Social Security Actuarial Assumptions (1998)  
    Edward A. Frees, FSA, Ph.D., Yueh-Chuan Kung, Ph.D., Siu-WanLan, ASA, Ph.D. Marjorie A. Rosenberg, FSA, Ph.D. and Virginia R.Young, FSA, Ph.D.
    Published in the October 1997 NAAJ.

Predictive Analytics

Risk Management

  • Application of Coherent Risk Measures to Capital Requirements in Insurance
    Philippe Artzner, Ph.D.
    The researcher reviewed the properties of coherent risk measures and examined their implications for capital requirement in insurance.
  • Aggregating Risks with Partial Dependence Information
    Fan Yang, Ph.D. and Daniël Linders, Ph.D.
    The researchers considered the problem of aggregating dependent risks in the presence of partial dependence information. 
  • An Insurance Risk Model with Parisian Implementation Delays
    David Landriault, FSA, FCIA; Jean-François Renaud, Ph.D, and Xiaowen Zhou, Ph.D.
    The researchers provided a realistic assessment of an insurer’s solvency risk.
  • Value Investing and Enterprise Risk Management: Two Sides of the Same Coin
    Max Rudolph, FSA, CERA, CFA, MAAA
    The researcher examined similarities between value investing and enterprise risk management methods.
  • A Hybrid Estimate for the Finite-time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization
    Qihe Tang, Ph.D. and Zhongyi Yuan, Ph.D.
    The researchers quantitatively analyzed extreme risk of insurance business in the presence of correlated insurance and financial risks, established approximations, examined their accuracy and applied the anticipated results in (a) to (b1) portfolio optimization with a constraint on a chosen risk measure and (b2) dynamic risk management.
  • Impact of Counter party Risk on the Reinsurance Market
    Michael Ludkovski, Ph.D. and Carole Bernard, Ph.D.
    The researchers investigated the impact of dependencies on the insurance contract design and optimal risk sharing in the reinsurance market.
  • Robust and Efficient Methods for Quantitative Risk Management
    Vytaras Brazauskas, Ph.D.
    The researcher attempted to discover if more sophisticated risk segmentation methods help to improve underwriting policy, pricing accuracy, and profitability.
  • Extreme Value Analysis for Partitioned Insurance Losses
    Ping-Hung Hsieh, Ph.D. and John B. Henry III
    The researchers specified a theoretically sound and defensible statistical model for analyzing extreme insurance losses in partitioned form, and consequently, provided useful and reliable summary statistics such as the conditional mean of extreme losses for decision making.
  • Levy Processes in Risk Theory  
    Jose Garrido, Ph.D., Dip., B.Sc., ASA and Manuel Morales
    The researchers investigated general risk models based on Levy Processes. The paper is published in the North American Actuarial Journal, October 2006, Vol. 10, Issue 4.
  • Asymptotic Behavior of Non-homogeneous Risk Processes and Ruin Probabilities
    Dr. Victor Korolev
    The researcher investigated the asymptotic properties of generalized risk processes in which the process of insurance claims is not a homogeneous Poission process as it is assumed in the classical theory. The research resulted in several papers, The Asymptotic Expansion for Qualities of Compoun dCox Processes and their Applications to Some Problems of Insurance and Financial Mathematics published in Theory of Probability and its Application, Volume 45, No. 1. It also produced Generalized Risk Processes.
  • An Actuarial Index of the Right-Tail Risk
    Dr. Shuan Wang, ASA
    The paper measures right tail risk by defining the right-taildeviation and the right tail index. The paper was published in the October 1998 NAAJ
  • Interaction Between Asset Liability Management and Risk Theory
    Dr. Jacques Janssen