Infinite Time Ruin Probability in the Individual Risk Model with Dependent Structure for Light and Heavy Tailed Distributions

We derive formulas for the moments of ruin time in a L\'evy risk model and use these to determine asymptotic behavior as initial capital tends infinity. In special case perturbed Cram\'er-Lundberg with phase-type or exponentially distributed claims, we explicitly compute first two time. All our considerations distinguish between profitable unprofitable setting.

Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities ψ(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.

Consider N players, respectively owning x1, x2, . . . , xN monetary units, who play a sequence of games, winning from and losing to each other integer amounts according to fixed rules. The sequence stops as soon as (at least) one player is ruined. We are interested in the ruin process of theseN players, i.e. in the probability that a given player is ruined first, and also in the expected ruin t...

Much research in ruin theory in insurance mathematics focuses on the behaviour of various quantities of interest, such as the probability of ruin or the ruin-time moments, for a particular risk model in insurance. In practice, precise knowledge of the risk model is available only via observed data. In this presentation, the problem of statistical estimation of the quantities of interest, given ...

In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integrodifferential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin...

This paper deals with optimal dividend payment problem in the general setup of a piecewise-deterministic compound Poisson risk model. The objective of an insurance business under consideration is to maximize the expected discounted dividend payout up to the time of ruin. Both restricted and unrestricted payment schemes are considered. In the case of restricted payment scheme, the value function...