Lévy processes under level-dependent Poisson switching
Abstract
Abstract In this paper we derive identities for the upward and downward exit problems and resolvents for a process whose motion changes between two Lévy processes if it is above (or below) a barrier b and coincides with a Poissonian arrival time. This can be expressed in the form of a (hybrid) stochastic differential equation, for which the existence of its solution is also discussed. All identities are given in terms of new generalisations of scale functions (counterparts of the scale functions from the theory of Lévy processes). To illustrate the applicability of our results, the probability of ruin is obtained for a risk process with delays in the dividend payments.
Fields of Study & Subjects
Probability and Risk Models
Stochastic processes and financial applications
Financial Risk and Volatility Modeling
Publication details
- Journal / source
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–34
- Publication date
- 10 April 2026
- Language
- EN