Corporate Finance Commons^™

Pricing Insurance Policies With A Distribution-Free Financial Pricing Model, Min-Ming Wen

Journal of Actuarial Practice (1993–2006)

The highly skewed and heavy tailed distributions used to model insurance losses (claims) raise a concern about the validity of the applications of the capital asset pricing model (CAPM) to insurance pricing when market risks are essential. This paper provides an alternative pricing model, called the Rubinstein-Leland model, which can be used to price insurance contracts. The Rubinstein-Leland model has a distribution-free feature that can fully capture the asymmetry embedded in insurance losses. Thus, this model is better able to derive fair prices for insurance policies than is the CAPM.

Bivariate Archimedean Copula Models For Censored Data In Non-Life Insurance, Michel Denuit, Oana Purcaru, Ingrid Van Keilegom

Journal of Actuarial Practice (1993–2006)

We describe a methodology based on Archimedean copulas for analyzing nonlife insurance data with censoring present. Specifically, we propose a graphical selection procedure for the nonparametric estimation of the generator. An actual loss-ALAE data set is used for the numerical illustrations and for comparisons of our approach to a few others.

Consistent Assumptions For Modeling Credit Loss Correlations, Jan Dhaene, Marc J. Goovaerts, Robert Koch, Ruben Olieslagers, Olivier Romijn, Steven Vanduffel

Journal of Actuarial Practice (1993–2006)

We consider a single period portfolio of n dependent credit risks that are subject to default during the period. We show that using stochastic loss given default random variables in conjunction with default correlations can give rise to an inconsistent set of assumptions for estimating the variance of the portfolio loss. Two sets of consistent assumptions are provided, which it turns out, also provide bounds on the variance of the portfolio's loss. An example of an inconsistent set of assumptions is given.

Journal Of Actuarial Practice, Volume 13, 2006, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

ARTICLES

Bivariate Archimedean Copula Models for Censored Data in Non-Life Insurance • Michel Denuit, Dana Purcaru, and Ingrid Van Keilegom 5

Bayesian Analysis of Insurance Losses Using the Biihlmann-Straub Credibility Model • Abraham J. van der Merwe and Kobus N Bekker . 33

Bayesian Analysis of a Health Insurance Model • Helio S. Migon and Edison M. O. Penna 61

Solvency of Life Insurance Companies: Methodological Issues • Rosa Cocozza and Emilia Di Lorenzo . 81

Pricing Insurance Policies with a Distribution-Free Financial Pricing Model • Min-Ming Wen . 103

A Note on the Instability of the Unprojected Individual Level …

Estimation Of Large Insurance Losses: A Case Study, Tine Buch-Kromann

Journal of Actuarial Practice (1993–2006)

This paper demonstrates an approach to analyzing liability data recently developed by a Danish insurance company. The approach is based on a Champernowne distribution, which is corrected with a non-parametric estimator. The correction estimator is obtained by transforming the data set with the estimated modified Champernowne cdf and then estimating the density of the transformed data set by using the classical kernel density estimator. Our approach is illustrated by applying it to an actual data set.

On Some Risk-Adjusted Tail-Based Premium Calculation Principles, Edward Furman, Zinoviy Landsman

Journal of Actuarial Practice (1993–2006)

This paper explores two tail-based premium calculation principles, the tail standard deviation (TSD) premium and the tail conditional expectation (TCE) premium, in their risk-adjusted and unadjusted forms. They are risk-adjusted using so-called distortion functions. We prove that the proportional hazard (PH) risk-adjusted TCE premium is larger than the unadjusted TCE premium. Additionally, given a risk distribution with location and scale parameters, we prove that the PH risk-adjusted TCE premium reduces to the unadjusted TSD premium.

Spatial Distribution Of Frequency And Severity Of Water Claims In California, Gurbhag Singh, Max Tang, Don Mcneill, Lyn Hunstad

Journal of Actuarial Practice (1993–2006)

We examine the frequency and severity of water loss claims for homeowners insurance across the state of California for the experience years 2000, 2001, and 2002. The spatial distribution patterns of frequencies and severities are mapped and analyzed at the zip code level. The maps reveal the pockets of high frequencies and severities. The information provided in this paper will assist actuaries and policy makers in their quest to set accurate rates for homeowners insurance.

Bayesian Analysis Of Insurance Losses Using The Buhlmann-Straub Credibility Model, Abraham J. Van Der Merwe, Kobus N. Bekker

Journal of Actuarial Practice (1993–2006)

We propose a Bayesian analysis to develop credibility estimates of the well known Biihlmann-Straub model. We describe simple numerical methods to obtain exact posterior distributions and predictive densities under this model. These distributions are obtained through Monte Carlo simulations that generate independent samples from the joint posterior distribution. Our methods are therefore preferable to methods such as Gibbs sampling, which generates dependent samples from the joint distribution. The methods discussed also can be extended to more complicated credibility models.

Analysis Of An Insurance Risk Model With Thinning Dependence And Common Shock, Lai Mei Wan, Kam Chuen Yuen, Wai Keung Li

Journal of Actuarial Practice (1993–2006)

We consider a continuous-time insurance risk model with m dependent classes of business with dependent claim number processes due to thinning dependence and a common shock. The impact of the dependence is studied via the adjustment coefficient. The case m = 2 is investigated analytically for exponential claim distributions and via simulation for non-exponential claim distributions.

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. …

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.

Optimal Dividend Strategies: Some Economic Interpretations For The Constant Barrier Case, Maite Marmol, M. Merce Claramunt, Antonio Alegre

Journal of Actuarial Practice (1993–2006)

We consider the surplus process of a non-life insurance portfolio with a dividend component represented by a constant dividend barrier strategy. The optimal dividend barrier is known when individual claim amounts follow an exponential distribution. This result for the optimal dividend barrier is used to develop combinations of the levels of the insurer's initial surplus and of the barrier which, under certain economic and financial criteria, can be regarded as optimal.

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.

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 …

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 …

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 New Hybrid Defined Benefit Plan Design, Wayne E. Dydo

Journal of Actuarial Practice (1993–2006)

Traditional defined benefit plans can be difficult to understand and complex to administer. Hybrid plans (cash balance and pension equity) arose in part to address the former issue, but at a price of greater administrative and litigation risk. I introduce a design for defined benefit pension plans that is easy to communicate to participants, allows for accrual patterns that closely replicate those of the two most common forms of hybrid pension plans, and avoids the controversial nondiscrimination issues that currently trouble sponsors of hybrid plans. The design defines the benefit as a fixed percentage of pay payable over a period …

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.

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 …

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 …

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.

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 …

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, …

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 …