Insurance Commons^™

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.

Journal Of Actuarial Practice, Volume 7, Nos. 1 And 2, 1999, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

ARTICLES

A Study Note on the Actuarial Evaluation of Premium Liabilities • Claudette Cantin and Philippe Trahan (First Prize)

Recognizing Actuarial Assumptions • Victoria Stachowski and Alice Underwood (Second Prize)

Commissioners Annuity Reserve Valuation Method (CARVM) • Keith P. Sharp (Third Prize)

CARVM and NAIC Actuarial Guidelines 33 & 34 • Keith P. Sharp

Multilife Premium Calculation with Dependent Future Lifetimes • Michel Denuit and Anne Cornet

A Fuzzy Approach to Grouping by Policyholder Age In General Insurance • Richard J. Verrall and Yakoub H. Yakoubov

Determination of Optimal Premiums as a Constrained Optimization Problem • Farrokh Guiahi

Credibility Calculations …

Using Parametric Statistical Models To Estimate Mortality Structure: The Case Of Taiwan, Shih-Chieh Chang

Journal of Actuarial Practice (1993–2006)

A mixture parametric model is used to analyze the changing pattern of Taiwanese mortality from 1926 to 1991. Three different age ranges are modeled as mixtures of extreme value distributions, namely the Weibull, inverse Weibull, and Gompertz distributions. The results show a significant improvement of mortality over the years.

Principles And Application Of Credibility Theory, Vincent Goulet

Journal of Actuarial Practice (1993–2006)

We review the history of the practical development of credibility theory. Emphasis is placed on the two main approaches to credibility theory: limited fluctuation credibility and greatest accuracy credibility. We explain when each approach should and should not be used. The presentation of greatest accuracy credibility theory starts with a review of (exact) Bayesian credibility and then moves to the Buhlmann-Straub model. Estimators of the structure parameters are discussed. Examples are presented to illustrate the concepts. Finally, the hierarchical credibility and crossed classification credibility models are presented.

Outlier Analysis Of Annual Retail Price Inflation: A Cross-Country Study, Wai-Sum Chan

Journal of Actuarial Practice (1993–2006)

Wilkie's stochastic investment model and its variants have been increasingly applied by actuaries around the world to actuarial modeling and simulation. This paper performs time series outlier analysis on retail price inflation, which is the driving force of Wilkie's composite model. The data come from four developed countries: the United Kingdom, the United States, Canada, and Australia. The fit of the model is significantly improved after the adjustment of outliers. The analysis also identifies exogenous events that have intervened in the inflation dynamics. An example is given to demonstrate the importance of outlier analysis on stochastic simulation. Finally, inflation trends …

Stability Of Representative Crediting Rate Scenarios Under Monte Carlo Simulations, Sarah L.M. Christiansen, Kelley Buchacker

Journal of Actuarial Practice (1993–2006)

We develop a methodology to ensure that a Monte Carlo simulation of the distribution of the primary rates, used for determining an interest crediting rate, is stable regardless of the initial random number seed. We consider the implications of the use of antithetic random normal deviates upon the scenario process and modifications to the candidate list and the choice function within the representative process. It is shown that the use of antithetic random deviates alone does not have a statistically significant effect on our results. The other two modifications (candidate selection algorithm and choice function) are statistically significant. Furthermore, the …

An Analysis Of Australian Pensioner Mortality By Pre-Retirement Income, David Knox, Andrew Tomlin

Journal of Actuarial Practice (1993–2006)

The existence of a relationship between an individual's socioeconomic status and his or her mortality is often accepted, but it is difficult to measure this relationship objectively. This study analyses the relationship between an individual's final salary immediately prior to retirement and mortality rates during retirement. The data used are taken from a large Australian public sector pension plan. A strong inverse relationship is found, which decreases with age. Some of the implications of these results for individual annuity markets and public pension policy are discussed.

A Frailty Model For Projection Of Human Mortality Improvements, Shaun S. Wang, Robert L. Brown

Journal of Actuarial Practice (1993–2006)

Based on the everyday observations that individual human beings vary significantly in their capacity to combat death, we adopt a so-called frailty model of human mortality. This frailty model assumes that each individual in a given population is endowed with his or her own frailty index, r, which remains constant for life. In addition, we assume that the individual's force of mortality (hazard rate function) at age x, Ux(r), satisfies Ux(r) = rUx where Ux is the population's base force of mortality at age x. Given the probability distribution of the frailty index among the newborns in the population, an …

Actuarial Techniques In Risk Pricing And Cash Flow Analysis For U.K. Bank Loans, Philip Booth, Duncan E.P. Walsh

Journal of Actuarial Practice (1993–2006)

A cash flow model is developed to set the price for a loan to a borrower with known risks. Similarities are noted between this model and those used for profit testing in life insurance. We emphasize aspects that reasonably can be treated in several ways and also indicate where the cash flow model differs from the pricing methods usually employed in bank lending. The sensitivity of interest rates to various parameters of the model such as the length of loan and the expected default rate is examined. Also, we examine how features of loans, including cash back and early repayments, …

Journal Of Actuarial Practice, Volume 6, Nos. 1 And 2, 1998, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

ARTICLES

Principles and Application of Credibility • Vincent Goulet

Actuarial Techniques in Risk Pricing and Cash Flow Analysis for U.K. Bank Loans • Philip Booth and Duncan E.P. Walsh

Stability of Representative Crediting Rate Scenarios Under Monte Carlo Simulations • Sarah L.M. Christiansen and Kelley Buchacker

Outlier Analysis of Annual Retail Price Inflation: A Cross-Country Study • Wai-Sum Cha

An Analysis of Australian Pensioner Mortality by Pre-Retirement Income • David Knox and Andrew Tomlin

Using Parametric Statistical Models to Estimate Mortality Structure: The Case of Taiwan • Shih-Chieh Chang

A Frailty Model for Projection of Human Mortality Improvements • Shaun …

No. 130 1997 November

International Journal for Business Education

SIEC Historical Documents

No. 129 1997 April

International Journal for Business Education

SIEC Historical Documents

A New Approach For Determining Claim Expense Reserves In Workers Compensation, Kay Rahardjo

Journal of Actuarial Practice (1993–2006)

This paper describes a new approach for determining a reserve for claim expenses. While the discussion focuses on workers compensation claims, the methodology is equally applicable to other lines of business. The approach also can be applied to the calculation of the reserve for all claims (including IBNR claims) and the reserve for claims reported to date (excluding IBNR claims). In addition, a methodology for pricing claims-handling services is discussed. The implications of pricing claims-handling services on a handle-to- conclusion basis versus pricing claims-handling services on a limited time handling basis are examined. Finally, the paper discusses a methodology for …

Providing Pensions For U.K. Employees With Varied Working Lives, Deborah R. Cooper

Journal of Actuarial Practice (1993–2006)

Several different working lives are investigated, including employees with breaks in employment, part-time employment, and temporary employment. The pensions that could be provided to the different employees by final salary, revalued career average, or money purchase pension schemes (plans) are calculated and compared. Some of the weaknesses in a final salary pension scheme (the treatment of deferred pensioners and cross subsidies between different groups of member) are considered. Possible alternative benefit structures are considered to address the problems.

Fuzzy Underwriting: An Application Of Fuzzy Logic To Medical Underwriting, Per-Johan Horgby, Ralf Lohse, Nicola-Alexander Sittaro

Journal of Actuarial Practice (1993–2006)

One of the most difficult issues in the medical underwriting of life insurance applicants is diabetes mellitus. Compiling the prognosticating parameters for diabetic applicants results in a complex system of mutually interacting factors. In addition, neither the prognosticating factors themselves nor their impact on the mortality risk is clear cut. We show how a fuzzy inference system can be used in underwriting diabetes mellitus. A fuzzy inference system can cope with the imprecise nature of medical parameters by converting them into fuzzy sets and aggregating them using mathematical techniques. The fuzzy underwriting system presented goes further than previous applications of …

Seeking The Profitability-Risk-Competitiveness Frontier Using A Genetic Algorithm, Ronnie Tan

Journal of Actuarial Practice (1993–2006)

Monte Carlo simulation is used to develop a flexible framework to measure the profitability, risk, and competitiveness of any insurance product. A genetic algorithm is then used to seek the optimum asset allocations that form the profitability-risk-competitiveness frontier and to examine the profitability, risk, and competitiveness trade-off's. We also show how to select the appropriate asset allocation and crediting strategy in order to position the product at the DeSired location on the profitability-risk-competitiveness spectrum.

Comments On Some Parametric Models For Mortality Tables, Kam C. Yuen

Journal of Actuarial Practice (1993–2006)

Parametric models for the entire age pattern of mortality have been suggested by Heligman and Pollard (1980) and Carriere (1992). The former is designed to fit the classical mortality pattern while the latter is supported by a statistical theory. Insights into their papers motivate us to consider a variation of the Heligman-Pollard model. We also apply these models to the 1993 Hong Kong Assured Lives Mortality Tables as well as the 1991 Hong Kong Female Life Table. This paper is not intended to construct a better parametric model for mortality tables; the main purpose is simply to provide insights into …