TITLE:
Optimal Proportional Reinsurance in a Bivariate Risk Model
AUTHORS:
Cristina Gosio, Ester C. Lari, Marina Ravera
KEYWORDS:
Collective Risk Theory, Optimal Proportional Reinsurance, Dynamic Programming
JOURNAL NAME:
Modern Economy,
Vol.6 No.6,
June
8,
2015
ABSTRACT: The paper deals with the optimal proportional reinsurance in a collective
risk theory model involving two classes of insurance business. These classes
are dependent through the number of claims. The objective of the insurer is to
choose an optimal reinsurance strategy that maximizes the expected exponential
utility of terminal wealth. We are able to derive the evolution of the insurer
surplus process under the assumption that the number of claims of the two
classes of the insurance business has a Poisson bivariate distribution. We face
the problem of finding the optimal strategy using the dynamic programming
approach. Therefore, we determine the infinitesimal generator for the surplus
process and for the value function, and we give the Hamilton Jacobi Bellmann
(HJB) equation. Under particular assumptions, we obtain explicit form of the
optimal reinsurance strategy on correspondent value function.