Abstract
We study the expected time to ruin in a risk process in which dividends are paid when the surplus is above the barrier. We consider the case in which the dividend rate is smaller than the premium rate. We obtain results for the classical compound Poisson risk process with phase-type claim size. When the ruin probability is 1, we derive the expected time to ruin and the expected dividends paid. When the ruin probability is less than 1, these quantities are derived conditioning on the event that ruin occurs.
| Original language | English |
|---|---|
| Pages (from-to) | 595-607 |
| Number of pages | 13 |
| Journal | Journal of Applied Probability |
| Volume | 42 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2005 |
Keywords
- Busy period
- Change of measure
- Fluid model
- Idle period
- Lundberg coefficient
- M/G/1 queue
- Martingale
- PH/M/1 queue
- Phase-type distribution
- Risk process
- Ruin probability
- Stopping time
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty