This paper concerns an optimal dividend distribution problem for an insurance company which risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The...

The {\em drawdown} process $Y$ of a completely asymmetric L\'{e}vy process $X$ is equal to $X$ reflected at its running supremum $\bar{X}$: $Y = \bar{X} - X$. In this paper we explicitly express in terms of the scale function and the L\'{e}vy measure of $X$ the law of the sextuple of the...

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...

For the Cramer-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in...