STABLE LEVY MOTION APPROXIMATION IN COLLECTIVE RISK THEORY

Collective risk theory is concerned with random fluctuations of the to tal net assets, the risk reserve, of an insurance company. In this pap er we consider weak approximations in risk theory which are especially relevant whenever the claim experience allows for heavy-tailed claims . We approximate the risk process by an alpha-stable Levy motion (1 < alpha < 2) with drift. The ruin probability within a finite time horiz on is estimated. Finally, a numerical example is presented. (C) 1997 E lsevier Science B.V.