Insurance Commons^™

Risk-Based Regulatory Capital For Insurers: A Case Study, Christian Sutherland-Wong, Michael Sherris

Journal of Actuarial Practice (1993–2006)

We study the issues in determining regulatory capital requirements using advanced modeling by assessing and comparing capital requirements under the two alternative approaches. A dynamic financial analysis (DFA) model is used for this case study. These issues are of current international interest as regulators, insurers, and actuaries face the significant issues involved with the introduction of risk-based capital for insurers.

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.

On The Pricing Of Top And Drop Excess Of Loss Covers, Jean-Francois Walhin, Michel Denuit

Journal of Actuarial Practice (1993–2006)

A top and drop cover is a treaty that can be found on the retrocession market. It offers capacity that can be used either to protect a top layer or a working layer. The former is called a "top" and the latter is called a "drop." Using the traditional collective risk model, we demonstrate the use of a multivariate version of Panjer's algorithm to price this cover. We also compare the premium obtained within the exact model with the premiums obtained either with the Frechet bounds or with the wrong assumption of independence.

Journal Of Actuarial Practice - Volume 12 (2005) - 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, Actuarial Frameworks ○ …

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 …

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.

A Modern Approach To Modeling Insurances On Two Lives, Maria Bilikova, Graham Luffrum

Journal of Actuarial Practice (1993–2006)

The analysis of life insurance contracts on two lives using the traditional deterministic approach has been an important part of actuarial education for the past fifty years or more. Recently there has been a shift from this deterministic approach to one using a more modern stochastic approach involving the future lifetime random variable. In this paper we will look at the problem using multiple-state models. In our view this approach allows a deeper analysis than either the traditional or the random future lifetime ones.

Ultimate Ruin Probability For A Time-Series Risk Model With Dependent Classes Of Insurance Business, Lai Mei Wan, Kam Chuen Yuen, Wai Keung Li

Journal of Actuarial Practice (1993–2006)

We consider a discrete-time risk model with m (m ~ 2) dependent classes of insurance business. The claim processes of these m classes are assumed to follow a multivariate autoregressive time-series model of order 1. Given this claims model, we explore the probability of ultimate ruin assuming exponentially bounded claims. As an example, we use simulations to study the case where there are two business and the underlying losses are of two types: bivariate exponential and bivariate gamma claim distributions.

Journal Of Actuarial Practice, Volume 12, 2005, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

ARTICLES

Risk-Based Regulatory Capital for Insurers: A Case Study • Christian Sutherland-Wong and Michael Sherris 5

A New Hybrid Defined Benefit Plan Design • Wayne E. Dydo . 47

A Primer on Duration, Convexity, and Immunization • Leslaw Gajek, Krzysztof Ostaszewski, and Hans-Joachim Zwiesler 59

Modeling Clusters of Extreme Losses • Beatriz Vaz de Melo Mendes and Juliana Sa Freire de Lima 83

Modeling Insurance Loss Data: The Log-EIG Distribution • Uditha Balasooriya, Chan Kee Low, and Adrian Y W Wong 101

A Modern Approach to Modeling Insurances on Two Lives • Maria Bilikova and Graham Luffrum 127

On the …

Obesity, Educational Attainment, And State Economic Welfare, Martin W. Sivula Ph.D.

MBA Faculty Conference Papers & Journal Articles

For the first time in history, estimates of the overweight people in the world rival estimates of those malnourished. The World Health Organization (WHO, 2002) ranked obesity among the top 10 risks to human health worldwide. In the early 1960s, nearly half of the Americans were overweight and 13% were obese. Today some 64% of U.S. adults are overweight and 30.5% are obese. Even more alarming, twice as many U.S. children are overweight than were twenty years ago, a 66% increase. Non-communicable diseases impose a heavy economic burden on already strained health systems. Health is a key determinant of development …

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, …

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 …

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 …

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.

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 …

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.

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 …

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 …

Sampling Concepts, Paul Boyd, Ph.D.

MBA Faculty Conference Papers & Journal Articles

The usefulness of any research is dependent upon how well the group studied represents the group about which decisions are to be made or conclusions drawn. That is, it depends upon how well the sample reflects relevant characteristics of the population. When it is possible to study every member of that group there is no problem, for on these occasions we can easily calculate the exact attribute (parameter) of interest for our population.

For example, if we were interested in determining the average number of gallons of gasoline sold to customers at our service station yesterday, we …

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 …

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.

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.

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 …

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.

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 …

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.