Robust risk control with reinsurance and CAT bonds

Abstract

This research studies robust risk control policies for an ambiguity-averse insurer. The insurer can manage its risk exposure through the purchase of reinsurance and the issuance of parametric catastrophe (CAT) bonds, which are linked to an exogenous trigger index. The insurer worries about the veracity of the model and seeks to develop a robust strategy to minimize the discounted ruin probability. We allow the insurer to exhibit different levels of ambiguity aversion toward its own claims and the trigger index. By employing a robust control approach, we analytically derive the optimal risk control policies that provide the insurer with guidelines on how to effectively manage its risk in an ambiguous environment. We present numerical examples that showcase scenarios in which CAT bonds can be utilized as an effective risk mitigation tool. Furthermore, we assess the potential welfare losses that could arise if the insurer fails to account for model uncertainty or lacks the ability to issue CAT bonds.