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Does Markov-Modulation Increase the Risk?

Published online by Cambridge University Press:  29 August 2014

Søren Asmussen ,
Andreas Frey ,
Tomasz Rolski  and
Volker Schmidt
Søren Asmussen*
Affiliation:
Aalborg University, Denmark
Andreas Frey*
Affiliation:
University of Ulm, Germany
Tomasz Rolski*
Affiliation:
University of Wroclaw, Poland
Volker Schmidt*
Affiliation:
University of Ulm, Germany
*
Institute of Electronic Systems, Aalborg University, Fr. Bajersv. 7, DK-9220 Aalborg, Denmark
Department of Stochastics, University of Ulm, Helmholtzstr. 18, D-89069 Ulm, Germany
Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Department of Stochastics, University of Ulm, Helmholtzstr. 18, D-89069 Ulm, Germany
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Abstract

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In this paper we compare ruin functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coefficients. The risk processes are as follows: in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate in the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes.

Keywords

Risk theorycompound Poisson modelMarkovian environmentstochastic orderingstop-loss orderingadjustment coefficientexponential tail orderingperturbation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 1 , May 1995 , pp. 49 - 66
Copyright
Copyright © International Actuarial Association 1995

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