Optimal Investment Problems with Uncertain Time Horizon
نویسندگان
چکیده
In this paper we consider an agent on a financial market who can trade with an uncertain time horizon by investing in risky stocks and a risk-free bond. He aims at maximizing the utility he draws from his final wealth measured by some utility function. We obtain a sufficient and necessary condition for the optimality, which gives an explicit expression for the optimal strategies as solutions of a new type of forward-backward stochastic differential equation (FBSDE). We also give an existence and uniqueness result for this kind of FBSDEs.
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