This paper deals with optimal investment and redistribution of the free reserves connected to life and pension insurance contracts in form of dividends and bonus. Formulated appropriately this problem can be viewed as a modification of Merton’s problem of optimal consumption and investment with a very particular form of consumption and utility hereof. Both are linked to a finite state Markov chain. We distinguish between utility optimization of dividends, where a semi-explicit result is obtained, and utility optimization of bonus payments. The latter connects to the financial notion of durable goods and allows for an explicit solution only in very special cases.

We provide necessary and sufficient conditions for optimality of mutual contracts for risk sharing under constraints on premiums or utility functions of participants of the agreement. These conditions are an extension of those of the Borch, Gerber and Bühlmann-Jewell ones. Some applications to optimal insurance contracts, optimal dividend sharing and optimal reinsurance are given.

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

In this note we consider how to maximise the adjustment coefficient in the case of proportional reinsurance. This complements some work of Waters (1983), where it was shown that there is a unique retention level maximising the adjustment coefficient. The advantage of our method is that only one implicit equation has to be solved.

In this paper a new methodology using the conditional specification technique intoduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas.

In this paper, we study the optimal asset allocation problem under a discrete regime switching model. Under the short-selling and leveraging constraints, the existence and uniqueness of the optimal trading strategy are obtained. We also obtain some natural properties of the optimal strategy. In particular, we show that if there exists a stochastic dominance order relationship between the random returns at different regimes, then we can order the optimal proportions we should invest in such regimes.

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

Different rating methods which allow for exceptional large claims are discussed. A robust Bayesian statistical model is proposed which can cope with non negative, skewed data. An example from fire insurance is analyzed. The performance of the posterior mean is compared to the performance of a robust credibility estimator.

We propose inference tools to analyse the concordance (or correlation) order of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a probability that two variables are simultaneously small or large at least as great as it would be were they left unspecified. Tests for its generalisation in higher dimensions, namely joint lower and upper orthant dominance, are also analysed. The parametric and semiparametric settings are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. A distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US insurance claim data.

Two families of frailty models – Makeham/Gompertz-gamma and Gompertz-inverse Gaussian – have been considered to graduate insurance-based mortality data. The aims of this exercise are twofold. The first aim is to make use of generalized linear models and to evaluate these against traditional techniques. The second aim is to measure the scale of individual heterogeneity in insurance-based populations. The results indicate that (subject to issues of identifiability) there is evidence of frailty in these populations.

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.

A method is introduced for testing the distribution of yield curves that are produced by asset scenario generators. The method is based on historical relationships in the conditional distributions of yield spreads given the short-term rate. As an illustration, this method is used to test a few selected models. To provide background, stochastic modeling for interest rates and fitting methods are briefly discussed.

A simple upper bound for the variance of the frequency estimates in a multivariate tariff using class criteria is deduced. This upper bound is based exclusively on univariate statistics and can, therefore, be calculated before a GLM analysis is carried out. It can be used to estimate the number of claims that will be needed for a tariff calculation depending on the number of tariff criteria and the number of levels of each criterion.

The article is a revised version of a paper presented at the XXXIst ASTIN Colloquium in Porto Cervo.