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Document Details :

Title: Optimal Dynamic Reinsurance
Author(s): DICKSON, David C.M. , WATERS, Howard R.
Journal: ASTIN Bulletin
Volume: 36    Issue: 2   Date: 2006   
Pages: 415-432
DOI: 10.2143/AST.36.2.2017928

Abstract :
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.