Optimal proportional reinsurance policies for diffusion models

Abstract

Abstract When applying a proportional reinsurance policy π the reserve of the insurance company is governed by a SDE =(aπ (t)u dt + aπ (t)σ dWt where {Wt } is a standard Brownian motion, µ, π, > 0 are constants and 0 ⩽ aπ (t) ⩽ 1 is the control process, where aπ (t) denotes the fraction, that is reinsured at time t. The aim of this paper is to find a policy that maximizes the return function Vπ (x) = where c > 0, τπ is the time of ruin and x refers to the initial reserve.