In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...

The Segerdahl-Tichy Process, characterized by exponential claims and state dependent drift, has drawn a considerable amount of interest, due to its economic interest (it is the simplest risk process which takes into account the effect of interest rates). It is also the simplest non-Lévy,...

As is well-known, the benefit of restricting Lévy processes without positive jumps is the “ W,Z scale functions paradigm”, by which the knowledge of the scale functions W,Z extends immediately to other risk control problems. The same is true largely for strong Markov processes X t , with...

Algorithms for simulation of a Lévy process X(t) are discussed, with particular emphasis on two algorithms approximating jumps that are in some sense small. One is classical, defining small jumps as those of small absolute value. The other one appears to be new and relies on an completely...