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A Primer On Duration, Convexity, And Immunization, Leslaw Gajek, Krzysztof Ostaszewski, Hans-Joachim Zwiesler

Journal of Actuarial Practice (1993-2006)

The concepts of duration, convexity, and immunization are fundamental tools of asset-liability management. This paper provides a theoretical and practical overview of the concepts, largely missing in the existing literature on the subject, and fills some holes in the body of research on the subject. We not present new research, but rather we provide a new presentation of the underlying theory, which we believe to be of value in the new North American actuarial education system.

Modeling Clusters Of Extreme Losses, Beatriz Vaz De Melo Mendes, Juliana Sa Freire De Lima

Journal of Actuarial Practice (1993-2006)

We model extreme losses from an excess of loss reinsurance contract under the assumption of the existence of a subordinated process generating sequences of large claims. We characterize clusters of extreme losses and aggregate the excess losses within clusters. The number of clusters is modeled using the usual discrete probability models, and the severity of the sum of excesses within clusters is modeled using a flexible extension of the generalized Pareto distribution. We illustrate the methodology using a Danish fire insurance claims data set. Maximum likelihood point estimates and bootstrap confidence intervals are obtained for the parameters and statistical premium. …

Modeling Insurance Loss Data: The Log-Eig Distribution, Uditha Balasooriya, Chan Kee Low, Adrian Y.W. Wong

Journal of Actuarial Practice (1993-2006)

The log-EIG distribution was recently introduced to the probability literature. It has positive support and a moderately long tail, and is closer to the lognormal than to the gamma or Weibull distributions. Our simulations show that data generated from a log-EIG distribution cannot be adequately described by lognormal, gamma, or Weibull distributions. The log-EIG distribution is a worthwhile candidate for modeling insurance claims (loss) data or lifetime data. Examples of fitting the log-EIG to published insurance claims data are given.

Reputation Pricing: A Model For Valuing Future Life Insurance Policies, Rami Yosef

Journal of Actuarial Practice (1993-2006)

The reputation of a life insurer is used to develop a model for determining the value of future life insurance policies. An M / G / 00 process is used to describe the sales and terminations (due to death or maturity) of future policies. The intensity of the arrival process is assumed to depend on the company's reputation. Explicit expressions are derived for the actuarial reserves and expected profits of these future policies.

An Application Of Control Theory To The Individual Aggregate Cost Method, Alexandros A. Zimbidis, Steven Haberman

Journal of Actuarial Practice (1993-2006)

The paper investigates the individual aggregate cost method (also known as the individual spread-gain method), which is normally applicable in small pension funds or fully contributory schemes, using a control theoretical framework. We construct the difference equations describing the mechanisms of the respective funding method and then calculate the optimal control path of the contribution rate assuming (first) a stochastic and (second) a deterministic pattern for the future investment rates of return. For the first case, the optimal solution is achieved through a linear approximation and using stochastic optimization techniques. It is proved that the contribution rate is (optimally) controlled …

Journal Of Actuarial Practice, Volume 11, 2004, Colin Ramsay , Editor

Journal of Actuarial Practice (1993-2006)

ARTICLES (the entire volume)

Product Innovation in Financial Services: A Survey • Christopher O'Brien 5

Phased Retirement for Defined Benefit Plan Participants • Patricia L. Scahill and Jonathan Barry Forman . 43

The Actuarial Value of Life Insurance Backdating • James M Carson and Krzysztof M Ostaszewski . 63

Decision Tree Analysis of Terminated Life Insurance Policies • Robert Keng Heong Lian, Yuan Wu, and Hian Chye Koh . 79

A Comparative Study of Parametric and Nonparametric Estimators of Old-Age Mortality in Sweden • Peter Fledelius, Montserrat Guillen, Jens Perch Nielsen, and Kitt Skovsø Petersen 103

Estimation of Complete …

Journal Of Actuarial Practice - Volume 11 (2004) - Contents And Masthead

Journal of Actuarial Practice (1993-2006)

Contents

Editorial Policy: Topics suitable for this journal include AIDS, annuity products, asset-liability matching, cash-flow testing, casualty rate making, credibility theory, credit insurance, disability insurance, expense analysis, experience studies, FASB issues, financial reporting, group insurance, health insurance, individual risk taking, insurance regulations, international issues, investments, liability insurance, loss reserves, marketing, pensions, pricing issues, product development, reinsurance, reserving issues, risk-based capital, risk theory, social insurance, solvency issues, taxation, valuation issues, and workers' compensation

Review Process

Editor - Colin Ramsay, University of Nebraska

Associate Editors: Robert Brown, University of Waterloo ○ Cecil Bykerk, Mutual of Omaha ○ Ruy Cardoso, …

Estimation Of Complete Period Life Tables For Singaporeans, Siu-Hang Li, Wai-Sum Chan

Journal of Actuarial Practice (1993-2006)

Complete period life tables, with death rates for every year of age, are not available in Singapore. This study constructs such tables for Singaporeans from the limited mortality information contained in the abridged life tables provided by the Singapore Department of Statistics. We find that linear interpolation, Whittaker graduation, and the Coale-Kisker method together can generate complete life tables that are smooth and continuous. The validity of the complete life tables generated by our method is further confirmed by (1) comparing the life expectancies calculated from our estimated life tables with those provided by the Singapore Department of Statistics, and …

Rapid Calculation Of The Price Of Guaranteed Minimum Death Benefit Ratchet Options Embedded In Annuities, Eric R. Ulm

Journal of Actuarial Practice (1993-2006)

This paper presents a new method of obtaining quick and accurate values and deltas for discrete look back options using Taylor series expansions. This method is applied to the case of ratchet guaranteed minimum death benefits attached to annuity contracts, and the method is extended to include annuities where a fixed fund is attached to the variable account. Finally, both the speed and the accuracy of the method are compared to Monte Carlo simulation and the exact analytic solution. The Taylor expansion method is shown to be faster and, in most cases, more accurate than the alternative methods.

Approximating The Bias And Variance Of Chain Ladder Estimates Under A Compound Poisson Model, Janagan Yogaranpan, Sue Clarke, Shauna Ferris, John Pollard

Journal of Actuarial Practice (1993-2006)

We consider the problem of estimating the outstanding claims produced by a homogeneous general insurance portfolio. The specific model considered in this paper is one where the number of claims in any loss period follows a Poisson distribution, settlement delays follow the same multinomial distribution, and settlements are single lump sums that are independent identically distributed random variables. Simulations using this model reveal that the development ratios and the outstanding claims estimates produced using the chain ladder method are positively biased. We obtain approximate formulas for the biases using Taylor series expansions of the random variables about their means. The …

Phased Retirement For Defined Benefit Plan Participants, Patricia L. Scahill, Jonathan Barry Forman

Journal of Actuarial Practice (1993-2006)

The demographic makeup of the U.S. workforce is changing. The population between ages SS and 64 is projected to increase significantly by 2020, but employment rates for this age group have not been increasing. Employers will likely need to encourage critical employees in this age group to delay retirement. Phased retirement is one tool for delaying retirement, while also not continuing full-time employment, so it can be a compromise for employers and employees. Both Congress and two administrative agencies have begun to consider changes in pension laws and regulations that would be needed to accommodate phased retirement for employers who …

The Actuarial Value Of Life Insurance Backdating, James M. Carson, Krzysztof Ostaszewski

Journal of Actuarial Practice (1993-2006)

Backdating is a common (and legal) practice in the U.S. whereby a life insurance contract bears a policy date that is prior to the actual application date. This practice often results in the opportunity for some insureds to reduce the annual premium paid. Using cash flow projections and U.S. mortality, lapse, and interest rate data, we provide a model of the actuarial value of term life insurance backdating. Results indicate that the benefits to the applicant of backdating a term life insurance policy increase as the applicant age (and hence premium) increases. Increasing mortality, lapse, and interest rates, as well …

Decision Tree Analysis Of Terminated Life Insurance Policies, Robert Keng Heong Lian, Yuan Wu, Hian Chye Koh

Journal of Actuarial Practice (1993-2006)

Statistical methods such as regression and survival analysis have traditionally been used to investigate the factors affecting the duration of terminated life insurance policies. This study explores a different approach: it uses a more recently developed data mining technique called decision trees. By sequentially partitioning the data to maximize differences in the dependent variable (duration in this study), the decision trees technique is good at identifying data segments with significant differences in the dependent variable. This identification can be useful when a company is trying to understand the factors driving or associated with the termination of life insurance policies. Decision …

Credibility Theory And Geometry, Elias S.W. Shiu, Fuk Yum Sing

Journal of Actuarial Practice (1993-2006)

We present a geometric approach to studying greatest accuracy credibility theory. Our main tool is the concept of orthogonal projections. We show, for example, that to determine the Buhlmann credibility premium is to find the coefficients of the minimum-norm vector in an affine space spanned by certain orthogonal random variables. Our approach is illustrated by deriving various common credibility formulas. Several equivalent forms of the credibility factor Z are derived by means of similar triangles.

A Comparative Study Of Parametric And Nonparametric Estimators Of Old-Age Mortality In Sweden, Peter Fledelius, Montserrat Guillen, Jens Perch Nielsen, Kitt Skovso Petersen

Journal of Actuarial Practice (1993-2006)

A recent study of Swedish old-age mortality used a modified GompertzMakeham model with a linear hazard for the force of mortality. We propose an alternative model using smooth two-dimensional kernel hazard estimators and introduce a new estimator based on the multiplicative bias correction for the multivariate marker dependent hazard. The multiplicative bias correction appears to have great potential for estimating mortality rates at the highest ages. We also observe that mortality continues to increase at an exponential rate even in old-age.

Product Innovation In Financial Services: A Survey, Christopher O'Brien

Journal of Actuarial Practice (1993-2006)

This paper considers product innovation in insurance and other financial services, an area where actuaries have an important role. It considers the proposition that there is no unique formula for success and that what works well in one situation may not work well in another. It first examines the sources of ideas for new products and, in particular, the role played by consumers, which is generally regarded as weak. It then looks at how ideas are implemented, with particular importance attributed to cross-functional teams and the formality of the product development process. Then it considers how success is measured (with …

Dynamic Funding And Investment Strategy For Defined Benefit Pension Schemes: A Model Incorporating Asset-Liability Matching Criteria, Shih-Chieh Chang, Cheng-Hsien Tsai, Chia-Jung Tien, Chang-Ye Tu

Journal of Actuarial Practice (1993-2006)

This paper studies the dynamic funding policy and investment strategy for defined benefit pension plans using one of the most comprehensive dynamic pension models to date. The model includes three investable assets: one risk free and two risky. The optimal plan decisions are formulated as a stochastic control problem that is solved using dynamic programming. The objective function uses performance measures to take into account the stability and solvency of the plan. The model is then applied to a Taiwanese pension.

Unearned Premiums And Deferred Policy Acquisition Expenses In Automobile Extended Warranty Insurance, Joseph Cheng

Journal of Actuarial Practice (1993-2006)

A prorata formula is commonly used to calculate unearned premium reserves in property-casualty insurance. I believe, however, that an exposure-adjusted formula is more appropriate in automobile extended warranties. This paper describes the exposure-adjusted approach to calculate the unearned premium reserves of an automobile extended warranty insurance program, to test the adequacy of the calculated reserves, and to determine the allowable deferred policy acquisition expenses from an insurance company's perspective.

Further Remarks On Risk Sources Measuring: The Case Of A Life Annuity Portfolio, Mariarosaria Coppola, Emilia Di Lorenzo, Marilena Sibillo

Journal of Actuarial Practice (1993-2006)

The paper considers a model that allows the actuary to measure the riskiness connected to the randomness of projected mortality tables in evaluating a portfolio of life annuities, obtaining a measure to reflect the risk associated with the randomness of the projection. The coherence of the risk parameters with the specific nature of the considered risk sources is also discussed. Numerical examples illustrate the results, showing the importance of the risk components in terms of the number of policies and comparing measure tools obtained by means of two procedures.

Improving Mortality: A Rule Of Thumb And Regulatory Tool, John H. Pollard

Journal of Actuarial Practice (1993-2006)

We develop a simple exact formula for determining cohort life expectancies under constant continuous uniform improvement in mortality using only a cross-sectional (period) Gompertz life table for the lives concerned and a simple approximation applicable to all life tables. The present values of annuities for such lives can be determined simply and accurately across the whole age span.

A Note On The Parallelogram Method For Computing The On-Level Premium, David P.M. Scollnik, Wai Man Sara Lau

Journal of Actuarial Practice (1993-2006)

This paper discusses the differences appearing in the descriptions of the parallelogram method for the determination of earned premium at current rate levels given by McClenahan (1996) and Brown and Gottlieb (2001). It observes that the former is consistent with the method of extending exposures while the latter is not. An illustration is provided. This paper also discusses two other approaches to the determination of the earned premium.

Model Risks And Surplus Management Under A Stochastic Interest Rate Process, Jennifer L. Wang, Rachel J. Huang

Journal of Actuarial Practice (1993-2006)

This paper uses simulations to explore the effects of incorrectly identifying the underlying interest rate process on assets, liabilities, and surplus levels. We show that mismodeling the interest rate (called model risk) could not only lead to a misstatement of the company's surplus, but could also cause a mismatch between the company's assets and liabilities. Our simulations demonstrate that three aspects of interest rates affect model risk: (i) volatility, (ii) level of long-term interest rate, and (iii) the speed at which the drift rate adjusts. We conclude that asset-liability managers should not ignore the impact of the model risks, regardless …

Journal Of Actuarial Practice, Volume 10, 2002, Colin Ramsay , Editor

Journal of Actuarial Practice (1993-2006)

ARTICLES

Communicating Effectively with Words, Numbers, and Pictures: Drawing on Experience • Karolina Duklan and Michael A. Martin

Unearned Premiums and Deferred Policy Acquisition Expenses in Automobile Extended Warranty Insurance • Joseph Cheng

Can Utility Maximization Models Assist With Retirement Planning? • Zaki Khorasanee

Dynamic Funding and Investment Strategy for Defined Benefit Pension Schemes: A Model Incorporating Asset-Liability Matching Criteria • Shih-Chieh Chang, Cheng-Hsien Tsai, Chia-Jung Tien, and Chang- Ye Tu

Model Risk and Surplus Management Under a Stochastic Interest Rate Process •Jennifer L. Wang and Rachel J. Huang

Some Comments on the Pricing of an Exotic Excess of …

Journal Of Actuarial Practice Volume 10 (2002) -- Contents And Masthead

Journal of Actuarial Practice (1993-2006)

Contents

Editorial Policy: Topics suitable for this journal include AIDS, annuity products, asset-liability matching, cash-flow testing, casualty rate making, credibility theory, credit insurance, disability insurance, expense analysis, experience studies, FASB issues, financial reporting, group insurance, health insurance, individual risk taking, insurance regulations, international issues, investments, liability insurance, loss reserves, marketing, pensions, pricing issues, product development, reinsurance, reserving issues, risk-based capital, risk theory, social insurance, solvency issues, taxation, valuation issues, and workers' compensation

Review Process

Editor - Colin Ramsay, University of Nebraska

Associate Editors: Robert Brown, University of Waterloo ○ Cecil Bykerk, Mutual of Omaha ○ Ruy Cardoso, …

Can Utility-Maximization Models Assist With Retirement Planning?, Zaki Khorasanee

Journal of Actuarial Practice (1993-2006)

Utility-maximization models for optimizing portfolio choices can be subdivided into two classes: those based on maximizing the expected utility of lifetime consumption and those based on maximizing the expected utility of retirement wealth. It is argued that the first type of model, which optimizes both saving and investment decisions, is difficult to apply in practice because of inadequate (or unreliable) information about individual preferences. Although the second type of model only optimizes investment decisions, it is of greater practical value because fewer data on individual preferences are required. The second type of model is used to derive formulae for the …

Communicating Effectively With Words, Numbers, And Pictures: Drawing On Experience, Karolina Duklan, Michael A. Martin

Journal of Actuarial Practice (1993-2006)

In this paper, we discuss techniques for developing effective communication skills, focusing in particular on technical writing, the use of graphics, and presentation. The key principles of effective communication that we propose to actuaries are as follows:

• Identify your audience and consider their needs and abilities;

• Focus on substantive content;

• Choose appropriate communication tools;

• Use language that is simple, concrete, and familiar;

• Integrate text, numbers, and graphics;

• Respond to information complexity creatively.

We focus in particular on the use of graphics as a communications tool as they are an efficient and potentially highly effective …

Modeling Size-Of-Loss Distributions For Exact Data In Winbugs, David P.M. Scollnik

Journal of Actuarial Practice (1993-2006)

This paper discusses how the statistical software WinBUGS can be used to implement a Bayesian analysis of several popular severity models applied to exact size-of-Ioss data. The particular models targeted are the gamma, inverse gamma, loggamma, lognormal, (two-parameter) Pareto, inverse (two-parameter) Pareto, Weibull, and inverse Weibull distributions. It is possible to implement additional size-of-Ioss models (including those for truncated data) using methods analogous to those described herein.

Some Comments On The Pricing Of An Exotic Excess Of Loss Treaty, Jean-Francois Walhin

Journal of Actuarial Practice (1993-2006)

This paper uses a multivariate analog of Panjer's algorithm to develop a method for pricing a complex excess of loss treaty. The treaty is such that some layers inure to the benefit of other layers. The structure of this treaty is discussed. Numerical examples are provided.

Exponential Bonus-Malus Systems Integrating A Priori Risk Classification, Llufs Bermudez, Michel Denuit, Jan Dhaene

Journal of Actuarial Practice (1993-2006)

This paper examines an integrated ratemaking scheme including a priori risk classification and a posteriori experience rating. In order to avoid the high penalties implied by the quadratic loss function, the symmetry between the overcharges and the undercharges is broken by introducing parametric loss functions of exponential type.

Analyzing Management Fees Of Pension Funds: A Case Study Of Mexico, Tapen Sinha

Journal of Actuarial Practice (1993-2006)

Though the rates of return for public pension funds have been high over the past two decades, one critical aspect of the financing of this type of fund is often overlooked: high management fees. As a result, the rates of return for workers who have invested in these funds have not necessarily been high. Management fees charged on pension funds in Mexico result in a leakage of funds in the order of 20-30% of the fund. That is, the amount at retirement would have been 20-30% higher had there been no fees. A model is developed that includes all the …