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.

Disability

• Optimal Disability Insurance with Moral Hazards: Absenteeism, Presenteeism, and Shirking
  Colin Ramsay, ASA, MAAA and Victor Oguledo
  The researchers developed a model of disability insurance that provides strategic policies that can incentivize employees to reduce presenteeism and absenteeism and mitigate the effects of moral hazard.

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)

Finance

• 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:
  • "Stochastic Life Annuities", which will be published in the North American Actuarial Journal, January 2007, Vol. 11, Issue 1
  • "Fitting Combinations of Exponentials to Probability Distributions", which will be published in Applied Stochastic Models in Business and Industry.
• 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:
  • "Pricing Options Using Lattice Rules" is published in the July 2005 NAAJ
  • "Valuation of the Reset Options Embedded in SomeEquity-Linked Insurance" is published in the July 2001 NAAJ.
• 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
  • In Bounding and Asymptotic Behavior of Ruin Probabilities in Collective Risk Theory: Final Report III, ARCH 1998.1, the results of the whole project are summarized along with the results on the last 1/3 of the research. Also in that article the other outcomes and locations from his research are listed.
  • The paper, Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison, proposes upper and lower bonds of ruin probabilities for the S. Anderson model with large claims and compares them. It was published in the October 1999 NAAJ.
• 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.
• Applications of Operations Research Methods to Solve Problems of Importance in Actuarial Science and Insurance Management
  Dr. Patrick Brockett
  The research develops and documents the applicability of operations research methodologies for improved global decision making in actuarial science and insurance management and to extend the theory and applications to insurance company management. The paper was published in the Transactions, 1995, Volume 47, Society of Actuaries.

Health

• 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.
• Statistical Methods for Monitoring HealthCare Process Measurements  
  Dr. Marjorie Rosenberg, FSA, MAAA
  Discusses the first step of quality control to monitor healthcare data. The article was published in the October 2001 NAAJ.

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.

Pensions

• 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

• A Spatial Cross-Sectional Credibility Model with Dependence Among Risks 
  Jimmy Poon, Yi Lu, Ph.D.
  The researchers obtained a linear form of prediction formulas for a generalized credibility model and explored estimation methods for structure parameters.
• What Actuaries Should Know About Nonparametric Regression With Missing Data
  Sam Efromovich, Ph.D.
  The researcher explored what can be done when observations miss traditional data used in nonparametric regression.
• A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims
  Liang Hong, Ph.D. and Ryan Martin, Ph.D.
  The researchers proposed a Dirichlet process mixture of log-normals model and discussed the theoretical properties and computation of the corresponding predictive distribution. 
• 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.
• Copula Regression
  Rahul Parsa, Ph.D.
  The researcher presented the formulas and algorithms necessary for conducting a copula regression analysis.
• An Asymptotic Analysis of the Bootstrap Bias Correction for the Empirical CTE
  N.D. Shyamalkumar, Ph.D, ASA
  The researcher theoretically studied existing estimators towards understanding their small sample behaviors.
• 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.
• Technologies Used in Modeling  
• Soft Computing Applications in Actuarial Science  
• Inflation-Parameter Family of Discrete Probability Distributions and their Application in Analysis of Over-and-Under Dispersed Insurance Data
  Dr. Nikolai Kolev, Ledi Minkova and Plamen Neytchev
  The project focused on constructing a new family of discreteprobability distributions which appear as an extension to thefamily of generalized power series distributions. The paper waspublished in ARCH, Volume 2000.1.
• Understanding Relationships Using Copulas(1998)
  Edward A. Frees, FSA, Ph.D., Emiliano Andreas P. Valdez,Ph.D.
  Published in the January 1998 NAAJ.

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