Robust optimal investment and reinsurance problems with learning

Abstract

In this paper, we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependency between them. The aim is to maximize the expected exponential utility of terminal wealth which is shown to imply a robust approach. We can solve this problem using a generalized HJB equation where derivatives are replaced by Clarke's generalized gradient. The optimal investment strategy can be determined explicitly and the optimal reinsurance strategy is given in terms of the solution of an equation. Since this equation is hard to solve, we derive bounds for the optimal reinsurance strategy via comparison arguments.