Optimal investment-reinsurance strategy with derivatives trading under the joint interests of an insurer and a reinsurer

Considering the common interests of an insurer and a reinsurer, the optimal investment-reinsurance problem with derivatives trading is studied. Suppose that both parties would invest a stock and a risk-free asset for capital appreciation, the insurer could purchase reinsurance and trade derivatives, the optimization problem is formulated by maximizing the expected exponential utility of two parties' wealth processes. The corresponding HJB equations are built for optimal strategy through the dynamic programming principle. In addition, derivatives trading is evaluated based on the certainty-equivalence principle. A numerical study directly illustrates how model parameters influence optimal strategies.