A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability...

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin. Compound Poisson processes with regime switching are used to model the surplus and the switching (a continuous-time controlled Markov chain) represents random environment...

This paper is concerned with the compound Poisson risk model and two generalized models with still Poisson claim arrivals. One extension incorporates inhomogeneity in the premium input and in the claim arrival process, while the other takes into account possible dependence between the successive...

This paper is concerned with the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard and Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard...

A financial institution that adopts an advanced measurement approach (AMA) as a method of computing operational risk capital has to measure 99.9 % value-at-risk (VaR) as the amount of an operational risk. The most popular method to satisfy the AMA standards requires the evaluation of aggregate...