考虑组合风险的指数化投资与随机线性二次最优控制

Risk Averting Index-based Investment and Stochastic Linear Quadratic Optimal Control

指数化投资使投资者享有市场平均收益水平,具有投资风险分散化、投资组合透明化、投资成本低廉等优势,日益受到投资者的亲睐.由于通常指数化投资者不愿意承担较大风险,本文考虑极小化跟踪误差与投资组合的风险之和(其中风险用风险资产的累积方差来衡量).本文证明了无论是连续时间或离散时间、有限时区或无限时区的情形,在一定的条件下,最优控制都唯一存在,即利用随机线性二次最优控制进行指数化投资,最优投资策略都唯一存在.

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 dis-crete 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.