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1991 | Buch

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Managing the Insolvency Risk of Insurance Companies

Proceedings of the Second International Conference on Insurance Solvency

herausgegeben von: J. David Cummins, Richard A. Derrig

Verlag: Springer Netherlands

Buchreihe : Catastrophe Modeling

Enthalten in: Professional Book Archive

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Two different applications have been considered, automobile claims from Massachusetts and health expenses from the Netherlands. We have fit 11 different distributions to these data. The distributions are conveniently nested within a single four parameter distribution, the generalized beta of the second type. This relationship facilitates analysis and comparisons. In both cases the GB2 provided the best fit and the Burr 3 is the best three parameter model. In the case of automobile claims, the flexibility of the GB2 provides a statistically siE;nificant improvement in fit over all other models. In the case of Dutch health expenses the improvement of the GB2 relative to several alternatives was not statistically significant. * The author appreciates the research assistance of Mark Bean, Young Yong Kim and Steve White. The data used were provided by Richard Derrig of The Massachusetts Automobile Rating and Accident Prevention Bureau and by Bob Van der Laan and The Silver Cross Foundation for the medical insurance claim data. 2~ REFERENCES Arnold, B. C. 1983. Pareto Distributions. Bartonsville: International Cooperative Publishing House. Cummins, J. D. and L. R. Freifelder. 1978. A comparative analysis of alternative maximum probable yearly aggregate loss estimators. Journal of Risk and Insurance 45:27-52. *Cummins, J. D., G. Dionne, and L. Maistre. 1987. Application of the GB2 family of distributions in collective risk theory. University of Pennsylvania: Mimeographed manuscript. Hogg, R. V. and S. A. Klugman. 1983. On the estimation of long tailed skewed distributions with actuarial applications.

Inhaltsverzeichnis

Frontmatter

Operational Models of Risk Assessment

Frontmatter

1. An Analysis of Underwriting Cycles and Their Effects on Insurance Solvency

Abstract

It is the conventional wisdom of the insurance industry the world over that the industry is subject to an underwriting cycle. By this is meant that the industry’s profit exhibits cyclical behaviour over time. In this context “profit” usually means total operating profit rather than just the underwriting profit component, though in the present paper it will not be necessary to focus on this distinction to any great extent.

Gregory Taylor

2. A Management Model of a General Insurance Company using Simulation Techniques

Abstract

The accounts of a general insurance company are not drawn up in such a way as to bring out the uncertainties involved in making an assessment of a company’s financial strength or of its future profit-earning capacity. Financial analysts attempt to infer the position from a careful examination of successive years’ accounts and the more detailed information available in returns to the supervisory authorities. A number of companies have developed a corporate planning process in which assumptions are made about future premium levels, volumes of business and profitability, and an attempt is made to follow this through to examine the impact on the balance sheet and future profits. However, in neither case is there an integrated model of the operations of the insurance company which takes uncertainty seriously into consideration.

C. D. Daykin, G. B. Hey

3. Classifying Financial Distress in the Life Insurance Industry

Abstract

Although life insurance insolvency has not been a serious problem in the past, the incidence of such insolvencies is increasing. The scope of this paper is to review the financial operations of life insurance companies in order to detect variables which will be helpful in identifying potential insolvencies. Three multivariate analyses are used in this paper: Multidiscriminant Analysis (MDA), nonparametric analysis and a logit analysis. The NAIC-IRIS Tests, the decomposition measures, and other financial ratios were found to be accurate measures for classifying failures in a multivariate framework one and two years prior to insolvency. The analyses correctly classified between 82 and 91 percent of the life insurance companies one and two years prior to insolvency. Cross-sectional validation on 31 publicly traded life insurers indicated that these large insurers are reasonably safe. All these life insurers were correctly classified as solvent companies. However, further analyses of these models and a prospective probability model indicates that more than one type analysis may be required for measuring the probability of failure.

Robert Hershbarger, Ran BarNiv

4. Variability of Pension Contributions and Fund Levels with Random Rates of Return

Abstract

Broadly, there are two types of pension funding methods, With individual funding methods (e.g. Projected Unit Credit and Entry Age Normal), the normal cost (NC) and the actuarial liability (AL) are calculated separately for each member and then summed to give the totals for the population under consideration. With aggregate funding methods (e.g. Aggregate and Attained Age Normal), there is no hypothecation of normal cost or actuarial liability to individuals; instead the group is considered as an entity, ab initio.

Steven Haberman, Daniel Dufresne

5. The Value of Ceded Reinsurance

Abstract

The purpose of this paper is to bridge part of the gap between actuaries and financial economists on the value of reinsurance. It is shown that a combined actuarial/financial approach will prove to be valuable for the reinsurance practice.

J. H. von Eije

6. Effect of Serially Autocorrelated Profit Margins on the Solvency of Insurers: The Case with Constant Target Margins Set by the Capital Asset Pricing Model

Abstract

Insurance ratemaking in the modern sense emphasizes the need for prices that are economically or financially appropriate in a competitive market. This emphasis manifests itself through procedures for estimating future costs per policy that are believed to produce unbiased estimates and through the selection of profit loadings that would lead to expected rates of return that are in economic equilibrium. This approach has been taken by Fairley [1979], Hill [1979], Kraus and Ross [1982], Myers and Cohn [1987]. It contrasts with older views, which tended to set the profit loading with the objective of limiting the probability of insolvency, as illustrated by Beard, Pesonen and Pentikainen [1984].

Emilio C. Venezian

7. Some Statistical Distributions for Insured Damages

Abstract

This paper considers a generalized four parameter statistical distribution as a model of losses, the generalized beta of the second kind (GB2). The distribution is very flexible and can model positive as well as negatively skewed data and also provides a model for thick and thin tailed distributions. The distribution provides an important structural interpretation in that it can accommodate unobservable heterogeneity. Heterogeneity is not imposed, but is accommodated by the model. The distribution includes such other important models encountered in the insurance literature as the lognormal, gamma, exponential, log-t and Burr distributions as special and limiting cases. Van der Laan [1987] provides a brief but excellent historical survey of a number of common distributions in modeling losses in insurance. Hogg and Klugman [1984] contains a careful development of alternative models and a treatment of estimation and inferential questions arising with loss distributions. The stable family of distributions has been considered by Paulson and Fair [1985].

James B. McDonald

Financial Models for Risk Assessment

Frontmatter

8. A Synthesis of Property-Liability Insurance Pricing Techniques

Abstract

Although the standard pricing model of the insurance industry (dating back to the 1921 National Convention of Insurance Commissioners (NCIC) Fire Insurance Committee report) ignores investment income in insurance ratemaking, many insurance pricing models have been proposed that integrate the underwriting and investment income aspects of the insurance contract. These models generally follow one of two distinct paths. Those proposed by insurance practitioners or academics specializing in insurance typically concentrate on the underwriting side of the insurance transaction and select rather arbitrary values for investment income. On the other hand, models developed by financial economists tend to concentrate on the investment aspect of insurance by emphasizing risk adjusted rates of return on investment while glossing over the specialized characteristics of the underwriting side of the insurance business. More recently, research has been aimed at developing pricing models that adequately address the importance of both underwriting and investment-related issues. The purpose of this paper is to compare and contrast the predictive abilities of a number of different insurance pricing models over an extended time period in order to demonstrate how the various models perform under different economic and competitive conditions. It is anticipated that this research will be of assistance to practitioners as well as academics in the application of insurance pricing models and interpretation of results.

James R. Garven, Stephen P. D’Arcy

9. Determining the Proper Interest Rate for Loss Reserve Discounting

Abstract

Property-liability loss reserves have been historically maintained at full undiscounted value, while life insurance reserves are discounted. Proponents of the undiscounted value argue that, unlike P/L loss reserves, life insurance benefits are relatively certain and thus more amenable to discounting, since the liability is quite likely to be realized. Others argue that the time value of money cannot be ignored, and all future liabilities should be discounted to properly reflect economic worth. As will be demonstrated in this paper, the views of both sides have merit and are incorporated into the proper result.

Robert P. Butsic

10. Safety Loadings for Loss Reserves

Abstract

The use of safety loadings for insurance premiums is well documented by insurance theory and practice. Using risk theory one can demonstrate that increasing the safety loading in the premium will decrease the probability of insolvency due to variation of incurred losses. However, many recognize that there are additional risks which are faced by insurance companies. Thus safety loadings for these additional risks may be justifiable.

Glenn Meyers

11. Rational Insurance Purchasing: Consideration of Contract Non-Performance

Abstract

Much of the analysis of rational insurance purchasing and hedging strategies has been undertaken on the basis of the expected utility hypothesis. This decision framework has been used to reformulate the Bernoulli principle that a risk averter rationally would fully insure at a fair premium. Other applications include the analysis of insurance at unfair premiums (Mossin [1968 ] and Smith [1968]), the effects of state-dependent utility on the rational insurance purchase (Cook and Graham [1977]), the effects of risky background wealth (Doherty and Schlesinger [1983] and Mayers and Smith [1983]), and the design of the optimal insurance policy (Raviv [1979] ). Such analyses have been conducted on the assumption that insurance policies are free of insolvency (default) risk. This assumption stands in sharp contrast to the actuarial literature in which the insolvency risk, or probability of ruin, is a central focus of attention.

Neil A. Doherty, Harris Schlesinger

12. Capital Structure and Fair Profits in Property-Liability Insurance

Abstract

Financial pricing models are becoming increasingly important in property-liability insurance. These models differ from traditional actuarial models by embedding the pricing decision in a market context so that the resulting prices are economically as well as mathematically consistent. Prices are established so that the return to equity capital of the insurer reflects the economy-wide price of risk.

J. David Cummins

Backmatter

Titel: Managing the Insolvency Risk of Insurance Companies
herausgegeben von: J. David Cummins
Richard A. Derrig
Verlag: Springer Netherlands
Electronic ISBN: 978-94-011-3878-9
Print ISBN: 978-94-010-5726-4
DOI: https://doi.org/10.1007/978-94-011-3878-9

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Operational Models of Risk Assessment

Frontmatter

1. An Analysis of Underwriting Cycles and Their Effects on Insurance Solvency

2. A Management Model of a General Insurance Company using Simulation Techniques

3. Classifying Financial Distress in the Life Insurance Industry

4. Variability of Pension Contributions and Fund Levels with Random Rates of Return

5. The Value of Ceded Reinsurance

6. Effect of Serially Autocorrelated Profit Margins on the Solvency of Insurers: The Case with Constant Target Margins Set by the Capital Asset Pricing Model

7. Some Statistical Distributions for Insured Damages

Financial Models for Risk Assessment

Frontmatter

8. A Synthesis of Property-Liability Insurance Pricing Techniques

9. Determining the Proper Interest Rate for Loss Reserve Discounting

10. Safety Loadings for Loss Reserves

11. Rational Insurance Purchasing: Consideration of Contract Non-Performance

12. Capital Structure and Fair Profits in Property-Liability Insurance

Backmatter