Optimal investment and premium control for insurers with ambiguity

Abstract

In this paper, we consider the optimal investment and premium control problem for insurers who worry about model ambiguity. Different from previous works, we assume that the insurer’s surplus process is described by a non-homogeneous compound Poisson model and the insurer has ambiguity on both the financial market and the insurance market. Our purpose is to find the impacts of model ambiguity on optimal policies. With the objective of maximizing the expected utility of terminal wealth, the closed-form solutions of the optimal investment and premium policies are obtained by solving HJB equations. Finally, numerical examples are also given to illustrate the results.

Keywords:

• expected utility
• HJB equation
• model ambiguity
• optimal investment
• premium control

Acknowledgements

The authors thank three anonymous referees and the editor for their careful reading and very useful comments that greatly improved the presentation of the paper. The research of the authors is supported by the National Natural Science Foundation of China (11571388), the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (15JJD790036), and the 111 Project (B17050).

Notes

1 In a probability space, two measures P and Q are equivalent, denoted by $Q\sim P$, if they have same null sets, i.e. Q(A) = 0 if and only if P(A) = 0.