Abstract
We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains C i (i = 1, 2, . . . ) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional gain feature; that is, if the surplus process just before the ith arrival is at level u, then for a > 0 the capital jumps up to the level (1 + a)u + Ci. The ruin probability and the distribution of the time to ruin are determined. We furthermore identify the value of discounted cumulative dividend payments, for the case of a Poisson arrival process of proportional gains. In the dividend calculations, we also consider a random perturbation of our basic risk process modeled by an independent Brownian motion with drift.
| Original language | English |
|---|---|
| Pages (from-to) | 549-580 |
| Number of pages | 32 |
| Journal | Advances in Applied Probability |
| Volume | 55 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2023 |
Funding
The research of O. Boxma was supported via a TOP-C1 grant from the Netherlands Organisation for Scientific Research. The research of E. Frostig was supported by the Israel Science Foundation, Grant No. 1999/18. The research of Z. Palmowski was supported by Polish National Science Centre Grant No. 2018/29/B/ST1/00756 (2019-2022).
Keywords
- dividend
- Dual risk model
- ruin probability
- time to ruin