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In this article, we study the optimal investment and reinsurance problem involving a defaultable security for a group which holds shares of both an insurance company and a reinsurance company. Assuming that the claim process is described by a Brownian motion with drift, and the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a risky asset and a defaultable bond. Moreover, the reinsurer is allowed to invest in a risk-free asset and a stock. With both the insurer and the reinsurer taken into account, the group aims to maximize the expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s terminal wealth. By using the dynamic programming approach, we study the pre-default case and post-default case, respectively. In both cases, the closed-form expressions for the optimal strategies and the corresponding value functions are derived. Finally, numerical examples are given to illustrate the effects of model parameters on the optimal strategies.

Optimal investment and reinsurance problem toward joint interests of the insurer and the reinsurer under default risk