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Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

A. Schöttl
A. Schöttl*
Affiliation:
Technical University of Munich
*
∗Postal address: Center of Mathematics Sciences, Technical University of Munich, D-80290 Munich, Germany
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Abstract

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.

Keywords

Risk reserve processoptimal stoppingMarkov modulationsmooth semimartingale representationinterest rates

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 115 - 123
Copyright
Copyright © Applied Probability Trust 1998 

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References

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