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...

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...

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 ...

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

A finite horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time Semi-Markov process (SMP) which ap...