Optimal reinsurance-investment problem with dependent risks based on legendre transform

Abstract

This paper investigates an optimal reinsurance-investment prob-lem in relation to thinning dependent risks. The insurer's wealth process is described by a risk model with two dependent classes of insurance business. The insurer is allowed to purchase reinsurance and invest in one risk-free asset and one risky asset whose price follows CEV model. Our aim is to maxi-mize the expected exponential utility of terminal wealth. Applying Legendre transform-dual technique along with stochastic control theory, we obtain the closed-form expression of optimal strategy. In addition, our wealth process will reduce to the classical Cramer-Lundberg (C-L) model when p = 0, in this case, we achieve the explicit expression of the optimal strategy for Hyperbolic Absolute Risk Aversion (HARA) utility by using Legendre transform. Finally, some numerical examples are presented to illustrate the impact of our model parameters (e.g., interest and volatility) on the optimal reinsurance-investment strategy.