Large claims approximations for risk processes in a Markovian environment

Søren Asmussen, Lotte Fløe Henriksen and Claudia Klüppelberg

Stochastic Processes and their Applications, 1994, vol. 54, issue 1, 29-43

Abstract: Let [psi]i(u) be the probability of ruin for a risk process which has initial reserve u and evolves in a finite Markovian environment E with initial state i. Then the arrival intensity is [beta]j and the claim size distribution is Bj when the environment is in state j[set membership, variant]E. Assuming that there is a subset of E for which the Bj satisfy, as x --> [infinity] that 1 - Bj(x) [approximate] bj(1 - H(x)); i.e. (1 - Bj(x))/(1 - H(x))-->bj [set membership, variant] (0, [infinity]), for some probability distribution H whose tail is subexponential density, and 1 - Bj(x) = o(1 - H(x)) for the remaining Bj, it is shown that for some explicit constant ci. By time-reversion, similar results hold for the tail of the waiting time in a Markov-modulated M/G/1 queue whenever the service times satisfy similar conditions.

Keywords: Risk; process; Markov; process; Asymptotic; ruin; probability; Non-cramer; case; Subexponential; distributions (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (7)

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