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.


  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • Managed Care and Health Care Utilization: Specification of Bivariate Models Using Copulas
  • Peng Shi, Ph.D, ASA and Wei Zhang, Ph.D.
  • The researchers studied the behaviors of participants in a health care system that consists of three key players, patients, health care provides, and insurance companies.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • Large Sample Behavior of the CTE and VaR Estimators under Importance Sampling
  • N.D. Shyamalkumar, Ph.D, ASA
  • The researcher brought to bear the state-of-the-art statistical theory upon the study and design of inference procedures for the CTE.
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  • Copula Regression
  • Rahul Parsa, Ph.D.
  • The researcher presented the formulas and algorithms necessary for conducting a copula regression analysis.
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  • An Asymptotic Analysis of the Bootstrap Bias Correction for the Empirical CTE
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  • N.D. Shyamalkumar, Ph.D, ASA
  • The researcher theoretically studied existing estimators towards understanding their small sample behaviors.
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  • 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.
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  • An Asymptotic Analysis of the Bootstrap Bias Correction for the Empirical CTE
  • Nariankadu Shyamalkumar, Ph.D, ASA
  • The researcher theoretically studied existing estimators towards understanding their small sample behaviors.
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  • 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.
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  • 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.
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  • 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 timesince this last minimum.
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  • 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.
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  • 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.
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  • The Optimal Allocation of Aggregate Mortality Risk
  • Anthony Webb
  • The researcher proposed a study of the aggregate mortality risk faced by annuity insurers.
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  • Inference for the Positive Stable laws Based on Special Quadratic Distance
  • Louis Doray, Ph.D, ASA
  • The researcher developed appropriate quadratic distance methods for estimating the parameters of the positive stable laws, based in the empirical Laplace transform or empirical probability generating function, and studied the asymptotic properties of this estimator,such as consistency and efficiency and the numerical implementation of the proposed techniques.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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:" Stochastic Life Annuities ", which will be published in the North American Actuarial Journal, January 2007, Vol. 11, Issue 1, and " Fitting Combinations of Exponentials toProbability Distributions", which will be published in Applied Stochastic Models in Business and Industry."
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  • 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.
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  • 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.
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  • 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 ARCH2006.1.
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  • Pricing of Guaranteed Annuity Conversion Options
  • Steven Haberman, FIA, ASA
  • The researcher presents a theoretical model (consistent with financial economics theory) for the pricingof 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.
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  • 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". Thepaper is published in the North American ActuarialJournal, January 2006, Vol. 10, Issue 1.
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  • Transferring the Financial Risks ofRetirement
  • 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 versionof the Retirement Income Calculator software.
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  • Mathematical Models and Software forFinancial Organizations at Risky Markets
  • Vladimir Morozov, Ph.D. and Alexander Vasin, Ph.D.
  • The researchers developed mathematical methods and software foraccumulation of the capital and investment portfolio managementproblems under specific conditions of the Russian financialmarkets. The paper was accepted for publication by theInternational Journal of Mathematics, Game Theory and Algebra.
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  • Real Longevity Insurance with aDeductible: An Introduction to Advanced-Life DelayedAnnuities  
  • Moshe Milevsky, Ph.D.
  • The researcher developed a better understanding of the economicpricing, efficiency and long-term evolution of the Canadian lifeannuity market, employing the modeling paradigm of continuous-timefinance theory. The paper is published in the October 2005NAAJ.
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  • Application of Quasi-Monte Carlo Methods to ActuarialScience
  • Phelim Boyle, FCIA, Ph.D. and Ken SengTan, ASA, Ph.D.
  • The project resulted in two research publications: " Pricing Options Using Lattice Rules" is published in the July 2005 NAAJ,and" Valuation of the Reset Options Embedded in SomeEquity-Linked Insurance " is published in the July 2001NAAJ.
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  • Credibility Using Copulas  
  • Edward(Jed) Frees, FSA, MAAA, Ph.D. and Ping Wang, Ph.D.
  • The researchers developed a direct link between credibility andloss distributions through the notion of a copula, a tool forunderstanding relationships among multivariate outcomes. The paperwas published in the April 2005 NAAJ.
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  • Valuation of Equity-Indexed Annuitiesunder 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.
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  • Contaminated Expotential Dispersion LossModels  
  • Professor Udi E. Makov and Professor Zinoviy Landsman
  • The research develops families of contaminated exponentialdispersion loss models and examined their theoretical propertiesand applicability to real heavy tailed loss data. It was publishedin the April 2003 NAAJ.
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  • Actuarial Aspects of Dependencies in InsurancePortfolios
  • 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
  • The Concept of Conomotonicity in Actuarial Science and Finance:Applications, Volume 31, Issue 2, October 2002.
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  • Robust and Efficient Fitting of Loss Models  
  • Dr. Robert Serfling
  • The researcher developed estimators which are both efficientand robust. The results are published in the October 2002NAAJ.
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  • Modern Modeling Technologies for PensionActuaries
  • Dr. Arnold F. Shaprio, EA, FSA, MAAA, MSPA
  • Several articles published in ARCH were a result of theresearch which investigated the role of modern modelingtechnologies for the pension actuary.
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Adaptive Nonlinear Models

Ed Lew was the 1973-74 president of The Societyof Actuaries and a longtime supporter of SOA efforts. He was anactive member and chairperson emeritus of the Committee on LifeInsurance Research at the time of his death in 1996. He was afounding member of the Actuarial Research Conference (ARC) and theActuarial Reserach Clearing House (ARCH) publication.

He had a longtime interest in modeling researchand was instrumental in providing the motivation for the beginningof the Society of Actuaries modeling conferences.

CKER administers this award program to advanceknowledge in actuarial modeling. The first awards were presented in1998.