Optimisation of drawdowns by generalised reinsurance in the classical risk model

Abstract We consider a Cramér–Lundberg model representing the surplus of an insurance company under general reinsurance control process. aim to minimise expected time during which is bounded away from its own running maximum by at least $$d>0$$ d > 0 (discounted preference rate $$\delta >0$$ δ ) choosing strategy. By analysing drawdown process (i.e. absolute distance controlled maximum) directly, we prove that value function fulfils corresponding Hamilton–Jacobi–Bellman equation and show how one can calculate optimal If initial critically large, problem corresponds maximisation Laplace transform passage time. constant retention level optimal. smaller than d , be expressed as element set Gerber–Shiu optimisation problems. these problems solved strategy feedback form. illustrate theory examples cases light heavy tailed claims.