Martingale and duality methods for optimal investment and reinsurance problem in a Lévy model

Abstract

In this paper, we employ the martingale and duality methods to study the optimal investment and proportional reinsurance problem for an insurer. The insurer’s risk process is modeled by a Lévy process and the capital can be invested in a security market described by a geometric Lévy process. The objective of the insurer is to maximize the expected utility of her terminal wealth. We derive the expression for optimal investment-reinsurance strategies for various utility functions. Furthermore, an example is considered, and numerical simulations are presented to illustrate the effect of the parameters on the optimal strategies.