Insurance Commons^™

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.

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.

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.

Fitting Loss Distributions In The Presence Of Rating Variables, Farrokh Guiahi

Journal of Actuarial Practice (1993–2006)

This paper focuses on issues and methodologies for fitting alternative statistical models-parametric probability distributions-to samples of insurance loss data. The interactions of loss distributions, deductibles, policy limits, and rating variables in the context of fitting distributions to losses are discussed. Fitted loss distributions serve an important function in pricing insurance products. The methodology developed in this paper is applied to a sample of insurance loss data that has the lognormal as the underlying loss distribution.

Linear Empirical Bayes Estimation Of Survival Probabilities With Partial Data, Mostafa Mashayekhi

Journal of Actuarial Practice (1993–2006)

In this paper we consider linear empirical Bayes estimation of survival probabilities with partial data from right-censored and possibly left-truncated observations. Such data are produced by studies in which the exact times of death are not recorded and the length of time that each subject may be under observation cannot exceed one unit of time. We obtain asymptotically optimal linear empirical Bayes estimators, with respect to the squared error loss function, under the assumption that the probability of death under observation in a unit time interval is proportional to the length of observation. This assumption is sometimes implied by Balducci's …

A Sensitivity Analysis Of The Premiums For A Permanent Health Insurance (Phi) Model, Ben D. Rickayzen

Journal of Actuarial Practice (1993–2006)

This paper presents an analysis of the parameters used in a multi-state model for permanent health insurance (PHI). The model is a simplification of that used in the United Kingdom. To avoid using duration dependent probabilities, the model splits the sick state into several sub-states to act as a proxy for duration spent in a particular state. This enables a Markov approach to be adopted. Lapses are incorporated within the model, and the net premium for a particular policy is tested for sensitivity to the various parameters used, including their interaction with the lapse rate. One of our conclusions is …

Controlling The Solvency Interaction Among A Group Of Insurance Companies, Alexandros Zimbidis, Steven Haberman

Journal of Actuarial Practice (1993–2006)

Pooling of risks is an efficient risk management technique used by large employee benefit schemes of multinational companies to self-insure their retirement and other benefit obligations. This technique forms a basis for formulating a general control theoretic model for the interaction between insurance companies within a pooling network. The objective of these insurance companies is to avoid insolvency yet maintain stable premium and surplus processes. A general control system of equations that is used as a model for the interaction of m insurance companies within the network is first analyzed. An analytic solution is provided. Questions concerning the stability and …

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.

Premium Earning Patterns For Multi-Year Policies With Aggregate Deductibles, Thomas Struppeck

Journal of Actuarial Practice (1993–2006)

MUlti-year policies with large aggregate deductibles or multiple triggers raise some interesting issues about the correct amount of unearned premium reserve that a company should carry. Examples in this paper illustrate some of the difficulties that arise when trying to establish such reserves. The basic approach taken here is that the pure premium portion of the unearned premium reserve should always be adequate to cover the remaining risk. This approach, however, can lead to some unusual and controversial earning patterns; there are even situations where a negative premium is earned. In addition, the earning pattern for a particular loss scenario …

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 …

Journal Of Actuarial Practice, Volume 9 (2001), Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

(The complete issue, including) ARTICLES

Analyzing Management Fees of Pension Funds: A Case Study of Mexico • Tapen Sinha 5

Premium Earning Patterns for Multi-Year Policies with Aggregate Deductibles • Thomas Struppeck 45

Exponential Bonus-Malus Systems Integrating A Priori Risk Classification • Lluis Benmidez, Michel Denuit, and Jan Dhaene 67

Fitting Loss Distributions in the Presence of Rating Variables • Farrokh Guiahi 97

Linear Empirical Bayes Estimation of Survival Probabilities with Partial Data • Mostafa Mashayekhi 131

Controlling the Solvency Interaction Among a Group of Insurance Companies • Alexandros Zimbidis and Steven Haberman 151

A Sensitivity Analysis of the Premiums …

Journal Of Actuarial Practice, Volume 8, Nos. 1 And 2 (2000) -- Masthead & Contents, Colin Ramsay , Editor

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, …

Journal Of Actuarial Practice, Volume 8, Nos. 1 And 2 (2000), Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

Complete volume, includes ARTICLES:

Realistic Pension Funding: A Stochastic Approach • Shih-Chieh Chang 5

Risk Sources in a Life Annuity Portfolio: Decomposition and Measurement Tools • Mariarosaria Coppola, Emilia Di Lorenzo, and Mari/ena Sibillo . .43

A Comparative Study of the Performance of Loss Reserving Methods through Simulation • Prakash Narayan and Thomas Warthen 63

Concentration in the Property and Liability Insurance Market by Line of Insurance • Edward Nissan and Regina Caveny 89

Safe-Side Requirements in Life Insurance: A Corporate Perspective • Annamaria Olivieri and Ermanno Pitacco 115

Actuarial Analysis of Retirement Income Replacement Ratios • Robert Keng Heong …

Modeling Corporate Bond Default Risk: A Multiple Time Series Approach, Wai-Sum Chan

Journal of Actuarial Practice (1993–2006)

A multiple time series approach is used to forecast the short-term u.s. corporate bond default level. These time series have two auxiliary economic variables: U.S. price inflation and U.S. GNP growth rate. Actual U.S. data from the turn of the century to the present are used to estimate the parameters of multivariate time series model. Diagnostic checks are performed to examine adequacy of the model. The model's forecast for the aggregate U.S. bond default level in 2000-2001 are 0.42% and 0.56%, respectively, while the forecast for the speculative-grade default rate in 2000 is 3.6%, which is more pessimistic than some …

Actuarial Analysis Of Retirement Income Replacement Ratios, Robert Keng Heong Lian, Emiliano A. Valdez, Chan Kee Low

Journal of Actuarial Practice (1993–2006)

A measure of level of post-retirement standard of living is the replacement ratio, i.e., percentage of final salary received as annual retirement income derived from savings. The replacement ratio depends on many factors including salary, salary increases, investment returns, and post-retirement mortality. Elementary life contingencies techniques are used to develop a replacement ratio formula and analyze its sensitivity to these factors.

Life Contingencies With Stochastic Discounting Using Moving Average Models, Steven Haberman, Russell Gerrard, Dimitrios Velmachos

Journal of Actuarial Practice (1993–2006)

This paper offers simplified procedures for calculating moments of functions in life contingencies when the random force of interest is modeled using an unconditional moving average process of order q, MA(q). It extends the MA(l) model that has been used for stochastic discounting. Using the more general MA(q) model allows actuaries to better capture the auto correlation between successive interest rates in a time series.

Independent Claim Report Lags And Bias In Forecasts Using Age-To-Age Factor Methodology, Stewart Gleason

Journal of Actuarial Practice (1993–2006)

This paper finds that when report lags are assumed to be independent, the age-to-age factor method produces biased estimates when applied to claim count development data. Two distributions are considered as models for the ultimate number of claims for an accident period: (0 a Poisson distribution, and (ii) a negative binomial distribution. In the Poisson case, the assumption of independent report lags implies the independence of the total number of claims reported in any two periods. In the negative binomial case, however, assuming that report lags are independent does not imply that increments are independent, and a somewhat different argument …

Concentration In The Property And Liability Insurance Market By Line Of Insurance, Edward Nissan, Regina Caveny

Journal of Actuarial Practice (1993–2006)

This paper uses an National Association of Insurance Commissioners (NAIC) 1995 data set to examine the concentration of property and liability insurance by line of insurance in the U.S. The primary measure of concentration used is the Herfindahl index. The largest 100 affiliates are divided into three largest sets of 20, 30, and 50. We find that the homeowners line is the most concentrated line and commercial auto physical damage is the least concentrated line, with the top 20 affiliates commanding the largest between-set and within-set contributions.

Risk Sources In A Life Annuity Portfolio: Decomposition And Measurement Tools, Mariarosaria Coppola, Emilia Di Lorenzo, Marilena Sibillo

Journal of Actuarial Practice (1993–2006)

The paper considers a model for a homogeneous portfolio of whole life annuities immediate. The aim is to study two risk factors: the investment risk and the insurance risk. A stochastic model of the rate of return is used to study these risk factors. Measures of the insurance risk and the investment risk for the entire portfolio are suggested. The problem of the longevity risk is presented, and its consequences with different projections of the mortality tables are analyzed. The model is applied to some concrete cases, and several illustrations show the importance of the two components of the riskiness …

A Comparative Study Of The Performance Of Loss Reserving Methods Through Simulation, Prakash Narayan, Thomas Warthen

Journal of Actuarial Practice (1993–2006)

Actuaries are often asked to provide a range or confidence level for the loss reserve along with a point estimate. Traditional methods of loss reserving do not provide an estimate of the variance of the estimated reserve, and actuaries use various ad hoc methods to derive a range for the indicated reserve. We use a Monte Carlo simulation method to compare various loss reserve estimation methods, including traditional methods and regression-based methods of loss reserving.

Safe-Side Requirements In Life Insurance: A Corporate Perspective, Annamaria Olivieri, Ermanno Pitacco

Journal of Actuarial Practice (1993–2006)

Safe-side requirements concern the assumptions used to calculate premiums in relation to a set of more realistic assumptions. Roughly, safe-side requirements express the capability of premiums to generate positive margins. In a strictly actuarial framework, safe-side requirements are given in terms of some notion of expected profit, calling for assumptions that let such profit be non-negative. An expected profit of zero, however, is not a realistic aim for the insurer. We investigate the notion of conservative assumptions by adopting a unconventional approach. Our focus is the management of the financial resources coming both from premiums and from shareholders' capital. This …

Realistic Pension Funding: A Stochastic Approach, Shih-Chieh Chang

Journal of Actuarial Practice (1993–2006)

The process funding pension plans is viewed as a dynamic control process. Two performance measures are introduced to evaluate the effectiveness of plan contributions: the cost-induced performance measure (CIPM) and the ratio-induced performance measure (RIPM). A dynamic programming approach is used to determining the optimal contributions with the objective of minimizing the performance measure. The methodology developed is applied to a sample of members of Taiwan's Public Employees Pension Plan (Tai-PERS). We show that RIPM produces more stable results than those using CIPM.

A Study Note On The Actuarial Evaluation Of Premium Liabilities, Claudette Cantin, Philippe Trahan

Journal of Actuarial Practice (1993–2006)

Several approaches have been used to estimate premium liabilities. The emphasis of these approaches has been on unearned premium and deferred policy acquisition expenses (DPAE), as such items represent the largest components of premium liabilities. The purpose of this paper is to provide a framework for the evaluation of premium liabilities and to augment the actuarial literature. We define and review the individual components of premium liabilities as well as the regulatory requirements and Canadian Institute of Actuaries recommendations and standards of practices related to premium liabilities. We also present an actuarial approach for estimating equity in the unearned premium, …

Commissioners Annuity Reserve Valuation Method (Carvm), Keith P. Sharp

Journal of Actuarial Practice (1993–2006)

This paper describes the commissioners annuity reserve valuation method (CARVM) and highlights the fundamental contrast with insurance valuation. Numerical examples illustrate methods of applying CARVM to particular annuity designs. The application of NAIC Actuarial Guideline 13 on bailouts is given particular attention.

Credibility Calculations Using Analysis Of Variance Computer Routines, Dennis H. Tolley, Michael D. Nielsen, Robert Bachler

Journal of Actuarial Practice (1993–2006)

In this paper we present a method of calculating Buhlmann-Straub credibility factors using standard statistical techniques developed for the analysis of variance. Emphasis is placed on using readily available statistical packages such as SAS and SPSS. Additionally many other computational tools such as EXCEL can be programmed to make such calculations. An example and some sample SAS programs are provided.

Determination Of Optimal Premiums As A Constrained Optimization Problem, Farrokh Guiahi

Journal of Actuarial Practice (1993–2006)

A simple stochastic model of an insurer's underwriting and related investment operations is used to determine the optimal amounts of written premiums for one period for the insurer's book of business. The written premium for each class is determined by the solution of a constrained optimization problem. The insurer's objective function is the expected profit on a book of business over the period. The insurer has a safety constraint where a certain portion of capital and surplus can be depleted with a small probability. This paper provides an explicit solution for optimum expected profit and corresponding written premiums by classes. …

A Fuzzy Approach To Grouping By Policyholder Age In General Insurance, Richard J. Verrall, Yakoub H. Yakoubov

Journal of Actuarial Practice (1993–2006)

In general insurance, policyholder age is often treated as a factor with the number of levels requiring that the individual ages of the policyholders be grouped. Although the groups are usually defined by the existing underwriting structure, it should be investigated as part of any premium rating exercise that uses a model to assess past claims experience. It is possible that an incorrect grouping by policyholder age could bias the results of the risk premium estimation. On the other hand, it may not be computationally feasible to use separate ages in the premium model, making some form of grouping necessary. …

Multilife Premium Calculation With Dependent Future Lifetimes, Michel Denuit, Anne Cornet

Journal of Actuarial Practice (1993–2006)

Actuaries traditionally have calculated multi-life (joint life) premiums by assuming the independence of the future lifetimes of insured persons. Recent studies, however, demonstrate dependence of the future lifetimes of couples (such as husbands and wives). This dependence materially affects the values of multi-life annuities and insurances. Using the Frechet-Hoeffding bounds and Norberg's Markov model, we determine the effect of this dependence in lifetimes on the actuarial present values of a widow's pension benefit.

Recognizing Actuarial Assumptions, Victoria Stachowski, Alice Underwood

Journal of Actuarial Practice (1993–2006)

As assumptions underlie every aspect of actuarial calculations, actuaries must be aware of the assumptions they are using and understand their importance and the possible effects of changing assumptions on the results of their calculations. This paper explores the nature of assumptions in: (i) mathematical models, (ii) data selection, (iii) actuarial methods, and (iv) the business environment. We examine reasons for making assumptions such as convenience, tradition, indications in the data, or lack of data. In addition, we discuss (i) how actuaries can judge whether these reasons are sufficient; (ii) methods that can help actuaries quantify the impact of their …

Carvm And Naic Actuarial Guidelines 33 & 34, Keith P. Sharp

Journal of Actuarial Practice (1993–2006)

Annuity valuation under the NAIC Standard Valuation Law is determined according to methods different from those methods used for life insurance. The CARVM assumption of efficient policyholder selection is clarified under NAIC Actuarial Guidelines 33 and 34 to allow for non-elective (e.g., death) benefits. In particular, Actuarial Guideline 34 is oriented toward variable annuities and prescribes methods to be used in the presence of a minimum guaranteed death benefit. In this paper these methods are examined and illustrated with examples.