A practical method is developed for computing moments of insurance functions when interest rates are assumed to follow an autoregressive integrated moving average process.

We present some relatively simple structural ideas about how probabilistic modeling, and in particular, the modern theory of point processes and martingales, can be used in the estimation of claims reserves.

This paper presents applications of stochastic control theory in determining an insurer's optimal reinsurance and rating policy. Optimality is defined by means of variances of such variables as underwriting result of the insurer, solvency margins of the insurer and reinsurer and the premiums paid by policy-holders.

This paper derives several formulas for the probability of eventual ruin in a discrete-time model. In this model, the number of claims process is assumed to be binomial. The claim amounts, premium rate and initial surplus are assumed to be integer-valued.

We consider a risk generating claims for a period of N consecutive years (after which it expires), N being an integer valued random variable. Let Xk denote the total claims generated in the kth year, k ≥ 1. The Xk's are assumed to be independent and identically distributed random variables, and are paid at the end of the year. The aggregate discounted claims generated by the risk until it expires is defined as where υ is the discount factor. An integral equation similar to that given by Panjer (1981) is developed for the pdf of SN(υ). This is accomplished by assuming that N belongs to a new class of discrete distributions called annuity distributions. The probabilities in annuity distributions satisfy the following recursion:

where an is the present value of an n-year immediate annuity.

The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.

The technique of risk invariant linear estimation from Neuhaus (1988) has been applied in the construction of a mutual quota share reinsurance pool between the subsidiary companies of the Storebrand Insurance Company, Oslo. The paper describes the construction of the reinsurance scheme.