232023 (M22, M10) Monte Carlo-simulation korrelierter zufallsvariabelen (Monte Carlo simulation of correlated random variables)

Abstract and Reviews of Melbourne, Research paper nr. 48, November 1997. In this paper the author presents a recursive method to compute moments of the time to ruin and the duration of the first period of negative surplus. This method uses a discrete time compound Poisson process used by Dickson et al. (1995). With this method he will be able to calculate approximations for the corresponding quantities in the classical model. Furthermore, for the classical compound Poisson model the paper considers some asymptotic formulae, as initial surplus tends to infinity, for he severity of ruin, which allows to find explicit formuale for the moments of the time of recovery.

Keywords: Probability of ruin, Compound Poisson model. 232021 (M13, M10)

Ruin Probabilities in the Presence of Heavy-Tails and Interest Rates Kliippelberg C., Stadtmiiller U., Scandinavian Actuarial Journal 1998, No. 1 The autors study the infinite time ruin probability for the classical Cram6r-Lundberg model, where the company also receives interest on its reserve. The authors consider the large claims case, where the claim size distribution F has a regularly varying tail. Hence our results apply for instance to Pareto, loggamma, certain Benktander and stable claim sie distribution. We prove that for a positive force of interest d, the ruin probability t~ (u) ~ K~I - F(u)) as the initial risk reserve u --> o0. This.® is different from the non-interest model, where i (u) ~ k j~. (1-F (y)) dy.

189

F~rster S., Deutsche Gesellschaft fiir Versicherungsmathematik, Band XXIII, Heft 3, April 1998. This paper describes a method for the Monte Carlo simulation of two correlated random variables. The author analyses linear combinations of stochastically independent random variables that are equally distributed over the interval (0, 1) ('random number') and also examines their distribution. F a suitable matrix of coefficients is chosen, the subsequent transformation results in random variables with the desired distribution properties and the given covariance. The method is carried out for a series of covariances using two exponentially distributed random variables.

Keywords: Monte Carlo Simulation, Covariances. PREMIUM, PREMIUM ORDERING OF RISKS

M30:

PRINCIPLES,

232024 (M30, M10)

On a Class of Premium Principles including the Esscher Principle Kamps U., Scandinavian Actuarial Journal 1998, No. 1 A class of premium calculation principles is considered with the premiums obtained as expected values of suitably transformed distribution functions. The Esscher principle is a particular example. It is found that the likelihood ratio ordering of risks is preserved for any of these principles. A renewal theoretic interpretation of a special principle is given, and useful properties as well as a related characterization of the exponential distribution are shown.

Keywords: Ruin probability, Infinite time.

Keywords: Premiums pinciples, Distribution functions, Esscher principle.

232022 (M13, M10)

M31:

Risk Pocesses Perturbed by a-stable L6vy Motion Furrer H., Scandinavian Actuarial Journal 1998, No. 1

232025 (M31)

The classical model of collective risk theory is extended in that an a-stable L6vy motion is added to the compound Poisson process. The convlution formula for the probability of ruin is derived. The author then investigates the asymptotic behaviour of the ruin probability as the initial capital becomes large.

Keywords: Collective risk theory, Ruin probability. M22: COMPUTER ORIENTED APPROACHES TO

RISK AND SIMULATION 232023 (M22, M10) Monte Carlo-Simulation korrelierter Zufallsvariabelen (Monte Carlo Simulation of correlated Random Variables)

EXPERIENCE RATING, CREDIBILITY THEORY, BONUS-MALUS SYSTEMS

Exponential Dispersion Models and Credibility Landsman Z., Makov U.E., Scandinavian Actuarial Journal 1998, No. 1 The Exponential Dispersion Family is a rich family of distributions, comprised of several distributions, some of which are heavy-tailed and as such could be of significant relevance to actuarial science. The family draws its richness from a dispersion parameter ¢r2= 1/k which is equal to 1 in the case of the Natural Exponential Family. The authors consider three cases. In the first ~. is assumed known, in the second a prior distribution for ~ is given, and in the third the prior distribution of L is not known and is derived by the means of the Maximum entropy principle, assuming the prior