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Optimal dynamic reinsurance

Dickson, David CM ; Waters, Howard R ( 2006-01)

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