Abstract
A Cox risk process with a piecewise constant intensity is considered where the sequence (Li) of successive levels of the intensity forms a Markov chain. The duration s, of the level Li is assumed to be only dependent via Li. In the small-claim case a Lundberg inequality is obtained via a martingale approach. It is shown furthermore by a Lundberg bound from below that the resulting adjustment coefficient gives the best possible exponential bound for the ruin probability. In the case where the stationary distribution of Li contains a discrete component, a Cramér-Lundberg approximation can be obtained. By way of example we consider the independent jump intensity model (Björk and Grandell 1988) and the risk model in a Markovian environment (Asmussen 1989).
Original language | English |
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Pages (from-to) | 196-210 |
Number of pages | 15 |
Journal | Journal of Applied Probability |
Volume | 33 |
Issue number | 1 |
Publication status | Published - Mar 1996 |
Keywords
- Change of measure
- Cox model
- Cramér-Lundberg approximation
- Lundberg inequality
- Martingale methods
- Risk theory
- Ruin probability