Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity

This study considers the optimal debt ratio and dividend payment policies for an insurer concerned about model misspecification. We assume that the insurer can invest all of its asset to the financial market and the ambiguity may exist in the risky asset. Taking into account the ambiguous situation, the insurer aims to maximize the expected utility of a discounted dividend payment until it ruins. Under some assumption, we prove that there exists classical solutions of the optimal debt ratio, dividend payment policies, and value functions that show that the existence of ambiguity can affect the optimal debt ratio and dividend policies significantly.