Abstract The Gerber-Shiu function provides a unified framework for the evaluation of a
variety of risk quantities. Ever since its establishment, it has attracted constantly increasing …

For a generalized scale function of standard processes, we characterize it as a unique
solution to a Volterra type integral equation. This allows us to extend it to an entire function …

In the last years there appeared a great variety of identities for first passage problems of
spectrally negative Lévy processes, which can all be expressed in terms of two “q-harmonic …

The threshold dividend strategy, under which dividends are paid only when the insurer's
surplus exceeds a pre-determined threshold, has received considerable attention in risk …

The scale functions were defined for spectrally negative L\'evy processes and other strong
Markov processes with no positive jumps, and have been used to characterize their …

In this paper, we study de Finetti's optimal dividend problem with capital injection under the
assumption that the dividend strategies are absolutely continuous. In many previous studies …

We study risk processes with level dependent premium rate. Assuming that the premium rate
converges, as the risk reserve increases, to the critical value in the net-profit condition, we …

Drawdown/regret times feature prominently in optimal stopping problems, in statistics
(CUSUM procedure), and in mathematical finance (Russian options). Recently it was …

We analyse an additive-increase and multiplicative-decrease (also known as growth–
collapse) process that grows linearly in time and that, at Poisson epochs, experiences …

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 …