TITLE:
Optimal Dynamic Proportional and Excess of Loss Reinsurance under Dependent Risks
AUTHORS:
Cristina Gosio, Ester C. Lari, Marina Ravera
KEYWORDS:
Reinsurance, Proportional Reinsurance, Excess of Loss Reinsurance, Hamilton-Jacobi-Bellman Equation
JOURNAL NAME:
Modern Economy,
Vol.7 No.6,
June
15,
2016
ABSTRACT: In this paper, we study an optimal reinsurance strategy combining a
proportional and an excess of loss reinsurance. We refer to a collective risk
theory model with two classes of dependent risks; particularly, the claim
number of the two classes of insurance business has a bivariate Poisson
distribution. In this contest, our aim is to maximize the expected utility of
the terminal wealth. Using the control technique, we write the
Hamilton-Jacobi-Bellman equation and, in the special case of the only excess of
loss reinsurance, we obtain the optimal strategy in a closed form, and the
corresponding value function.