Article contents
Expansions for Markov-modulated systems and approximations of ruin probability
Published online by Cambridge University Press: 14 July 2016
Abstract
Let N be a stationary Markov-modulated marked point process on ℝ with intensity β∗ and consider a real-valued functional ψ(N). In this paper we study expansions of the form Eψ(N) = a0 + β∗a1 + ·· ·+ (β∗)nan + o((β∗)n) for β∗→ 0. Formulas for the coefficients ai are derived in terms of factorial moment measures of N. We compute a1 and a2 for the probability of ruin φ u with initial capital u for the risk process in the Markov-modulated environment; a0 = 0. Moreover, we give a sufficient condition for ϕu to be an analytic function of β∗. We allow the premium rate function p(x) to depend on the actual risk reserve.
Keywords
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1996
Footnotes
Work supported by KBN under grant 2 1023 90 01.
References
- 4
- Cited by