The Stochastic Characteristics of Property-Liability Insurance Company Underwriting Profits

Cummins, J. David; Nye, David J.

doi:10.2307/252682

Cited by 31 publications

(12 citation statements)

References 12 publications

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“…Both normal and lognormal density functions have been used to describe the insurer's aggregate loss distribution (cf. Cummins and Nye [6]), as well as other distributions. Since the probabilities of insolvency and tax‐shield redundancy are at issue, some prudent curve fitting should influence the choice of regulatory model.…”

Section: A Numerical Illustrationmentioning

confidence: 90%

Price Regulation in Property‐Liability Insurance: A Contingent‐Claims Approach

Doherty¹,

Garven

1986

The Journal of Finance

175

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A Discrete time option pricing model is used to derive the "fair" rate of return for the property liability firm. The rationale for the use of this model is that the financial claims of the policyholders have the characteristics of a European call option written on the firm's asset portfolio. By setting the value of this option equal to the initial surplus, an implicit solution for the fair insurance price may be derived. This approach does not require the direct estimation of risk premiums and thereby offers both analytic and practical advantages over existing methods.

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Section: A Numerical Illustrationmentioning

confidence: 90%

Price Regulation in Property‐Liability Insurance: A Contingent‐Claims Approach

Doherty¹,

Garven

1986

The Journal of Finance

175

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“…However, property-liability insurance claims at the firm level can be highly skewed and heavy-tailed (Cummins et al 1990;McNeil 1997), implying that equity returns for property-liability insurers will not be normally distributed either. For example, Cummins Downloaded by [University of Arizona] at 19:21 18 September 2015 and Harrington (1988) document significant levels of skewness in insurance stock returns for a sample of property-liability companies for the time period 1970-1983 (see also Cummins and Nye 1980). Similar findings are reported for the life insurance sector (see, for example, Gentry and Pike 1970;Harrington 1983).…”

Section: Actuarial Sciencementioning

confidence: 53%

Skewed distributions in finance and actuarial science: a review

Adcock

Eling

Loperfido

2012

The European Journal of Finance

125

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That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research. C. Adcock et al.those of Arditti and Levy (1975) and Kraus and Litzenberger (1976), marks the point at which the modern theory of finance started revealing evidence of skewness analogous to that provided by Markowitz, Sharpe, Lintner, Tobin, and others.In the context of actuarial science, it is important to recognize that insurance risks have skewed distributions (see, for example, Lane 2000), which is why in many cases, the classical normal distribution is an inadequate model for insurance risks or losses. Some insurance risks also exhibit heavy tails, especially those exposed to catastrophes (see Embrechts, McNeil, and Straumann 2002). The skew-normal distribution and its extensions thus might be promising since they preserve the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. The skew-normal distribution and its extensions have been used recently in studies on risk management, capital allocation, and goodness-of-fit (Vernic 2006;Bolance et al. 2008;Eling 2012).This review paper is motivated by the belief that asymmetry in asset returns, and skewness in particular, is an important field of research. Such research has two clear themes. The first is the never-ending and entirely natural wish to develop better univariate models for asset returns. Such model developme...

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“…We conclude by looking at the impact of a change in the correlation structure. Empirical studies tend to show that there are significant autocorrelations between the claims of the various periods (see Cummins and Nye, 1980, and for the German insurance market, Maurer, 2000, p. 226). Moreover, it seems reasonable to assume that there is a positive correlation between the loss development for prior‐year claims and the net claims in the current year.…”

Section: A Simulation Model Based On Empirical Datamentioning

confidence: 99%

New Risk‐Based Capital Standards in the European Union: A Proposal Based on Empirical Data

Schmeiser

2004

Risk Manage Insurance Review

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In response to criticism concerning the current solvency system, the European Commission is developing new rules for insurance companies operating in the member states of the European Union (EU). Under this so-called Solvency II concept, an insurer is allowed to verify its solvency by using an internal risk management model previously approved by the regulatory authority. In this article we develop such an internal risk management approach for propertyliability insurers that is based on dynamic financial analysis (DFA). The proposed concept uses a simulation technique and models the central risk factors from the investment and underwriting areas of an insurance company. On the basis of the data provided by a German insurer, the ruin probabilities under different scenarios and varying planning horizons are calculated.

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The Stochastic Characteristics of Property-Liability Insurance Company Underwriting Profits

Cited by 31 publications

References 12 publications

Price Regulation in Property‐Liability Insurance: A Contingent‐Claims Approach

Price Regulation in Property‐Liability Insurance: A Contingent‐Claims Approach

Skewed distributions in finance and actuarial science: a review

New Risk‐Based Capital Standards in the European Union: A Proposal Based on Empirical Data

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