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Corrected Diffusion Approximations for Ruin Probabilities in a Markov Random Walk

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

C. D. Fuh
C. D. Fuh*
Affiliation:
Academia Sinica
*
∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, Republic of China. Research partially supported by NSC 84-2121-M-001-025.
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Abstract

Let (X, S) = {(Xn, Sn); n ≧0} be a Markov random walk with finite state space. For a ≦ 0 < b define the stopping times τ= inf {n:Sn > b} and T= inf{n:Sn∉(a, b)}. The diffusion approximations of a one-barrier probability P {τ < ∝ | Xo= i}, and a two-barrier probability P{ST ≧b | Xo = i} with correction terms are derived. Furthermore, to approximate the above ruin probabilities, the limiting distributions of overshoot for a driftless Markov random walk are involved.

Keywords

DIFFUSION APPROXIMATIONLADDER HEIGHT DISTRIBUTIONMARKOV-DEPENDENT WALD MARTINGALEMARKOV RANDOM WALKGAMBLER'S RUIN

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60K15: Markov renewal processes, semi-Markov processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 695 - 712
Copyright
Copyright © Applied Probability Trust 1997 

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