Portfolio selections for insurers with ambiguity aversion: minimizing the probability of ruin

In this paper, we investigate the impacts of model misspecification on the insurer’s investment behaviours. Model misspecification comes from either the financial market or insurance business due to economic fluctuation. From the risk control point of view, we assume that an insurer has ambiguity aversion and we study the robust optimal investment strategy for the insurer under several settings. As a benchmark, we firstly obtain the optimal investment strategy for the insurer without considering model misspecification. Then, by assuming that model misspecification only exists in the financial market, we obtained the robust optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the objective of minimizing the probability of ruin. The results tells us the insurer’s ambiguity aversion leads to a more conservative investment behaviour. At last, we incorporate the model misspecification for both financial market and insurance business in a general framework. The robust optimal investment is also obtained and we find that the investment is enlarged due to the insurer’s ambiguity aversion on the insurance business because of the motivation of ambiguity hedging. The numerical examples display that different ambiguity aversion level on the financial market and insurance business have different impacts on the robust investment strategy.