Expansions for Markov-modulated systems and approximations of ruin probability
- 1 March 1996
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 33 (1) , 57-70
- https://doi.org/10.2307/3215264
Abstract
LetNbe a stationary Markov-modulated marked point process on ℝ with intensityβ∗and consider a real-valued functionalψ(N). In this paper we study expansions of the formEψ(N) =a0+β∗a1+ ·· ·+ (β∗)nan+o((β∗)n) forβ∗→ 0. Formulas for the coefficientsaiare derived in terms of factorial moment measures ofN. We computea1anda2for the probability of ruinφuwith initial capitalufor the risk process in the Markov-modulated environment;a0= 0. Moreover, we give a sufficient condition forϕuto be an analytic function ofβ∗. We allow the premium rate functionp(x) to depend on the actual risk reserve.Keywords
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