Completed CKER Projects

Mortality Improvement Cohorts and the Effect on the Annuities Market and Social Security System in the United State
Krzysztof Ostaszewski and Richard MacMinn, Illinois State University, in response to mortality improvement, are studying special cohorts and correlations among them in various countries and their effect on prices of retirement instruments.

The Distribution of the Sum of Lognormals
Daniel Dufresne, University of Melbourne, worked on pricing lognormals, with a particular emphasis on the numerical application of the theoretical results to the pricing of Asian and basket options. This resulted in two papers. "Stochastic Life Annuities" will be published in the North American Actuarial Journal, vol. 10, No. 4, October 2006. "Fitting Combinations of Exponentials to Probability Distributions" will be published in Applied Stochastic Models in Business and Industry.

Levy Processes in Risk Theory
Jose Garrido and Manuel Morales, Concordia University, Montreal, Canada, investigated general risk models based on Levy Processes. The paper will be published in the North American Actuarial Journal, vol. 10, No. 3, July 2006.

Valuation of Equity-Indexed Annuities under Stochastic Interest Rate
by Dr. Sheldon Lin, ASA and Dr. Ken Seng Tang, ASA
In the October 2003 North American Actuarial Journal, the researchers discuss the pricing of equity-indexed annuities. An abstract of the article can be found at

Contaminated Exponential Dispersion Loss Models  
by Professor Udi E. Makov and Professor Zinoviy M. Landsman
The research published in the North American Actuarial Journal, Volume 7, Number 2, April 2003, develops families of contaminated exponential dispersion loss models and examined their theoretical properties and applicability to real heavy tailed loss data.

Actuarial Aspects of Dependencies in Insurance Portfolios

by 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 Comonotonicity in Actuarial Science and Finance: Applications," Volume 31, Issue 2, October 2002.

Robust and Efficient Fitting of Loss Models
by Dr. Robert Serfling
The researcher developed estimators which are both efficient and robust. The results are published in the North American Actuarial Journal, Volume 6, Number 4, October 2002.

Modern Modeling Technologies for Pension Actuaries

By Dr. Arnold F. Shapiro, 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.
"Adaptive Nonlinear Models"
"The Inner Workings of Neural Networks and Genetic Algorithms"
"Technologies Used in Modeling"
"Soft Computing Applications in Actuarial Science"

Generalized Cox, Ingersoll and Ross Model: Statistics and Valuation of Interest Rate Derivatives
by Dr. Wojciech Szatazchneider
He presents a simple construction of the extended Cox, Ingersoll & Ross model for term structure of interest rate, and a simple way of pricing general interest rate derivatives with this model which can be found in the Mexican Journal of Economics and Finance, Volume 1, Number 4, 2002 

The Cost of Mismatch in Stochastic Interest Rate Models
by Dr. Michel Jacques, ASA
Evaluated the cost of mismatch by a percentile of the cash flow distribution when interest rates follow a stochastic model.

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?" Published in the Scandinavian Actuarial Journal, Volume 2000, Number 2/September 1, 2000.

Inflation-Parameter Family of Discrete Probability Distributions and their Application in Analysis of Over- and Underdispersed Insurance Data
by Dr. Nikolai Kolev, Ledi Minkova, and Plamen Neytchev
The project focused on constructing a new family of discrete probability distributions which appear as an extension to the family of generalized power series distributions.

Tight Approximation of Basic Characteristics of Classical and Non-Classical Surplus Processes
by 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.

Valuation of Credit Line Commitments Subject to Credit Risk 
by Dr. Daniel Dufresne, FSA and J.P. Chateau
In the paper, "Pricing the Put Option of Bank Credit Commitments: A Two-Factor Model of Credit Risk," the researchers examine prime-rate loan commitments with a floating-rate formula devised as "stochastic index cost of funds plus a fixed forward mark-up."

Asymptotic Behavior of Non-homogeneous Risk Processes and Ruin Probabilities
by Dr. Victor Korolev
The researcher investigated the asymptotic properties of generalized risk processes in which the process of insurance claims in not a homogeneous Poission process as it is assumed in the classical theory. This research resulted in several papers, "The Asymptotic Expansions for Qualities of Compound Cox 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."

Pricing Practices for Joint Last Survivor Insurance
by 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.

Statistical Methods for Monitoring Health Care Process Measurements
by Dr. Marjorie Rosenberg, FSA, MAAA
To develop the first step of quality control to monitor health care data.

Credibility Using a Loss Function From Spline Theory: Practical Considerations
by Dr. Virginia Young, FSA
Reviews and expands previous research by developing ways to use results to calculate expected claims.

Bounding and Asymptotic Behavior of Ruin Probabilities in Collective Risk Theory
by Dr. Vladimir Kalashnikov
In "Bounding and Asymptotic Behavior of Ruin Probabilities in Collective Risk Theory: Final Report III," ARCH 1998, Volume 1, the results of 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.

One of the resulting papers, "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.

An Actuarial Index of the Right-Tail Risk
by Dr. Shuan Wang, ASA
The paper proposes to measure right tail risk by defining the right-tail deviation and the right tail index.

Is Social Security a Regressive System?
by Dr. Robert L. Brown, ACAS, FCIA, FSA
This paper analyzes both the Old-Age, Survivors, and Disability Insurance (OASDI) system of the US and the Canada/Quebec Pension Plans (C/QPP) in Canada to determine whether these systems are "a good deal" and whether they are regressive or progressive.

The 1996 Accidental Death Mortality Table: A Comprehensive Analysis of Recent Accidental Death Experience
by Jay Jaffe, FCIA, FSA, MAAA
For actuaries interested in accidental death mortality, 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 for US business.

Interaction Between Asset Liability Management and Risk Theory
by Dr. Jacques Janssen
The resulting paper measures risks when the value of the liabilities becomes larger than the value of the assets.

Random Mortality Rates and the Analysis of Selective Lapsation
by Dr. Bruce Jones, FCIA, FSA
Researches 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.

Statistical Methods of Combining Multiple Sets of Count Data
by Dr. H. Dennis Tolley, ASA and Dr. Gilbert Fellingham
The purpose of the research was to examine statistical methods of estimating lapsation rates as they apply to guaranteed issue health insurance policies. One of the resulting papers, "Combining Life Table," 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.

A Stochastic Model of the Asset Liability Management
by Dr. Lijia Guo, ASA
The research addresses the stochastic modeling for managing asset liability process.

The Analysis of CCRC Data
by 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.

Pricing Decisions in Insurance: A Fuzzy Logic Approach
by 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 Rules that Consider Statistical Data," and
"Insurance Rate Changing: A Fuzzy Logic Approach," Journal of Risk and Insurance, September 1996, Volume 63, Number 3.

Methodology to Deal with Dependencies on Multi-Life Risks

by 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," investigates the use of models of dependent mortality for determining annuity values.

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.

Public Employees Retirement Systems
by Michael Samet, EA, FCA, FSA, MAAA, Timothy Peach, EA, FSA, MAAA, 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).

Applications of Operations Research Methods to Solve Problems of Importance in Actuarial Science and Insurance Management
by 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.

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