Investment And Consumption Of Jump-Diffusion Model Under Time-Inconsistent Discount Assumption

Merton portfolio management problem las been widely studied, and many extend results have been obtained. In this paper, we consider the problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the investment and consumption decision. Besides, we assume that the price of risk asset follows the jump-diffusion. We will apply the optimal control theory to seek the subgame-perfect equilibrium strategy defined in [1]. We can get the necessary condition for optimal strategy if the control set is convex and close, we can also get the sufficient condition for equilibrium strategy.In Chapter 2, we briefly introduce the involved concepts and basic theory. In Chapter 3. we formulate the time-inconsistent investment and consumption problem under jump-diffusion price process. In Chapter 4, we obtain the necessary condition of optimal strategy and sufficient condition for equilibrium strategy and give out the proof of the two cases.