A New Stochastic Model For Stock Price with Delay Effects

摘要

In this paper, we consider a portfolio optimization problem over an infinite time horizon, in which a new model with delay effects is used to describe the stock price. The problem is formulated as a stochastic control problem in which the goal is to maximize total expected discounted utility by choosing the optimal investment and consumption controls. Dynamic programming method is used to derive the Hamilton-Jacobi-Bellman equation and then the existence and uniqueness results for log utility case are established.