Optimal proportional reinsurance policies for diffusion models

Abstract

When applying a proportional reinsurance policy π the reserve of the insurance company is governed by a SDE =(aπ(t)udt + 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. © 1998 Scandinavian University Press.