关键词: 指数化投资, 随机线性二次最优控制, 反馈控制, 无限时区

Abstract: This paper focuses on the index tracking problem with the investor's risk aversion taken into account. We try to minimize the weighted sum of tracking error and portfolio risk which is assumed to be the accumulated variance of the risk asset in the portfolio process. The main conclusion is that whether it is for continuous or discrete case, finite or infinite time zone, under certain conditions, the optimal control will uniquely exist. In other words, the optimal investment strategy is available by using stochastic optimal control for index-based investment.

Key words: index-based investment, stochastic linear quadratic optimal control, feedback control infinite, time zone