We consider an alternative to the usual credibility premium that arises from squared-error loss, namely, a so-called equitable credibility premium (Promislow and Young, 1999). We derive formulas for the credibility weight in certain cases and give sufficient conditions for exact credibility.

Young (1999) discussed the conjecture proposed by Christofides (1998) regarding the premium principle of Wang (1995, 1996). She shows that this conjecture is true for location-scale families and for certain other families, but false in general. In addition Young (1999) states that it remains an open problem to determine under what circumstances Wang's premium principle reduces to the standard deviation (SD) premium principle.

In this paper we will provide further discussion of this problem. We will show that, for a fixed distortion, the natural set on which Wang's premium principle can reduce to the SD premium principle is and only is the union of location-scale families which satisfies some condition. Furthermore, it will be shown that the natural set is and only is a location-scale family if Wang's premium principle can be reduced to the SD premium principle for any distortion.

This paper discusses the modelling and control of pension funds.

A continuous-time stochastic pension fund model is proposed in which there are n risky assets plus the risk-free asset as well as randomness in the level of benefit outgo. We consider Markov control strategies which optimise over the contribution rate and over the range of possible asset-allocation strategies.

For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. Furthermore, the asset allocation strategy always lies on the capital market line familiar from modern portfolio theory.

A general quadratic loss function is proposed which provides an explicit solution for the optimal contribution and asset-allocation strategies. It is noted that these solutions are not dependent on the level of uncertainty in the level of benefit outgo, suggesting that small schemes should operate in the same way as large ones. The optimal asset-allocation strategy, however, is found to be counterintuitive leading to some discussion of the form of the loss function. Power and exponential loss functions are then investigated and related problems discussed.

The stationary distribution of the process is considered and optimal strategies compared with dynamic control strategies.

Finally there is some discussion of the effects of constraints on contribution and asset-allocation strategies.

This paper proposes a multivariate generalization of the generalized Poisson distribution. Its definition and main properties are given. The parameters are estimated by the method of moments.

Alzheimer's disease (AD) accounts for a significant proportion of long-term care costs. The recent discovery that the ε4 allele of the ApoE gene indicates a predisposition to earlier onset of AD raises questions about the potential for adverse selection in long-term care insurance, about long-term care costs in general, and about the potential effects on costs of gene therapy, or better targetted treatments for AD. This paper describes a simple Markov model for AD, and the estimation of the transition intensities from the medical and epidemiological literature.

In the present paper we extend a recursive algorithm developed by Vernic (1999) for compound distributions with bivariate counting distribution and univariate severity distributions to more general multivariate counting distributions.

We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral . For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.

In this paper we study some bivariate counting distributions that are obtained by the trivariate reduction method. We work with Poisson compound distributions and we use their good properties in order to derive recursive algorithms for the bivariate distribution and bivariate aggregate claims distribution. A data set is also fitted.

This paper explains securitization of insurance risk by describing its essential components and its economic rationale. We use examples and describe recent securitization transactions. We explore the key ideas without abstract mathematics. Insurance-based securitizations improve opportunities for all investors. Relative to traditional reinsurance, securitizations provide larger amounts of coverage and more innovative contract terms.

Based on the profit and loss account of an insurance company we derive a probabilistic model for the financial result of the company, thereby both assets and liabilities are marked to market. We thus focus on the economic value of the company.

We first analyse the underwriting risk of the company. The maximization of the risk return ratio of the company is derived as optimality criterion. It is shown how the risk return ratio of heterogeneous portfolios or of catastrophe exposed portfolios can be dramatically improved through reinsurance. The improvement of the risk return ratio through portfolio diversification is also analysed.

In section 3 of the paper we analyse the loss reserve risk of the company. It is shown that this risk consists of a loss reserve development risk and of a yield curve risk which stems from the discounting of the loss reserves. This latter risk can be fully hedged through asset liability matching.

In section 4 we derive our general model. The portfolio of the company consists of a portfolio of insurance risks and of a portfolio of financial risks. Our model allows for a simultaneous optimization of both portfolios of risks. A theorem is derived which gives the optimal retention policy of the company together with its optimal asset allocation.

Some of the material presented in this paper is taken from Schnieper, 1997. It has been repeated here in order to make this article self contained.