In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to determining hitting probabilities for the solution to a randomly perturbed s...

In this paper we discuss the classical risk process that is perturbed by diffusion. We prove some properties of the supremum distribution of the risk process before ruin when ruin occurs and the surplus distribution at the time of ruin. We present the simple and explicit expression for these distributions when the claims are exponentially distributed. ©2000 Published by Elsevier Science B.V. Al...

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical CramerLundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-...

Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber–Shiu...

This paper investigates the probability of ruin within finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset. Under assumption that the risks are heavy tailed, some precise estimates for the finite time ruin probability are derived, which confirm a folklore that the ruin probability is mainly determined by whichever o...