Catastrophe Insurance and Optimal Investment

In the insurance market, the insurers who provide catastrophe insurance face with the risk of rare, but huge catastrophe claims. The introduction of catastrophe related securities into the marketplace provide the insurers the instruments to hedge some of the catastrophe risks they are facing. A catastrophe related security is tied to the prespecified catastrophe claims, while independent to other claims. It is the ties between the catastrophe related securities and the catastrophe insurance claims that make the catastrophe related securities special to the insurers. The catastrophe securities and the insurance claims are not just correlated each other but simply bounded together for those claims specified in the catastrophe securities. However, the insurers cannot trade away the risk of those claims that are not covered by the catastrophe securities, because the catastrophe related securities do not cover every possible claim. In other words, the catastrophe insurance market is incomplete. Therefore, this partial tie characterizes the relation between the catastrophe securities and the claims. The partial tie poses a different optimal investment problem, what is the best policy to participate in the catastrophe security market, for a catastrophe insurer. In this paper we study the optimal investment policy for the insurers in the business ∗Sheen Liu is at Vancouver and Gene Lai is at Pullman campus.