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Optimal Dynamic Reinsurance

Published online by Cambridge University Press:  17 April 2015

David C.M. Dickson  and
Howard R. Waters
David C.M. Dickson
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia, E-mail: dcmd@unimelb.edu.au
Howard R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Great Britain, Email: H.R.Waters@ma.hw.ac.uk
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Abstract

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We consider a classical surplus process where the insurer can choose a different level of reinsurance at the start of each year. We assume the insurer’s objective is to minimise the probability of ruin up to some given time horizon, either in discrete or continuous time. We develop formulae for ruin probabilities under the optimal reinsurance strategy, i.e. the optimal retention each year as the surplus changes and the period until the time horizon shortens. For our compound Poisson process, it is not feasible to evaluate these formulae, and hence determine the optimal strategies, in any but the simplest cases. We show how we can determine the optimal strategies by approximating the (compound Poisson) aggregate claims distributions by translated gamma distributions, and, alternatively, by approximating the compound Poisson process by a translated gamma process.

Keywords

Finite time ruinreinsurancedynamic strategytranslated gamma distributiontranslated gamma process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 415 - 432
Copyright
Copyright © ASTIN Bulletin 2006

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