Optimal consumption, investment and insurance with insurable risk for an investor in a Levy market

Numerous researchers have applied the martingale approach for models driven by Levy processes to study optimal investment problems. The aim of this paper is to apply the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Levy processes and the utility is a constant absolute risk aversion (CARA). The model developed in this paper can potentially be applied to absorb large insurable losses in the absence of insurance protection and to examine the level of diminishing current utility and consumption. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.