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Lundberg inequalities for a Cox model with a piecewise constant intensity

Part of: Markov processes Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Hanspeter Schmidli
Hanspeter Schmidli*
Affiliation:
Heriot-Watt University
*
∗Postal address: Actuarial Maths & Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
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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 σi 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).

Keywords

COX MODELRUIN PROBABILITYLUNDBERG INEQUALITYCRAMER–LUNDBERG APPROXIMATIONRISK THEORYMARTINGALE METHODSCHANGE OF MEASURE

MSC classification

Primary: 60H99: None of the above, but in this section
Secondary: 60G44: Martingales with continuous parameter 60J99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 196 - 210
Copyright
Copyright © Applied Probability Trust 1996 

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