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Some asymptotic results for transient random walks with applications to insurance risk

Part of: Markov processes Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Aleksandras Baltrūnas
Aleksandras Baltrūnas*
Affiliation:
Institute of Mathematics and Informatics, Vilnius
*
∗ Postal address: Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Email address: [email protected]
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Abstract

We consider a real-valued random walk which drifts to -∞ and is such that the step distribution is heavy tailed, say, subexponential. We investigate the asymptotic tail behaviour of the distribution of the upwards first passage times. As an application, we obtain the exact rate of convergence for the ruin probability in finite time. Our result supplements similar theorems in risk theory.

Keywords

transient random walkssubexponential distributionsprecise large deviationsruin probability

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 60K25: Queueing theory
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G51: Processes with independent increments; L'evy processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 108 - 121
Copyright
Copyright © by the Applied Probability Trust 2001 

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