An optimization of a continuous time risk process

Abstract

A continuous time risk process is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an action is taken, either an investment to other business when the level of surplus reaches V > 0 or an injection of capital when the surplus goes below tau(0 < tau < V). After assigning several costs related to managing the surplus, we obtain the long-run average cost per unit time. A numerical example is studied. (C) 2009 Elsevier Inc. All rights reserved.