基于线性学习函数的泛证券投资组合策略

最优定常再调整策略所产生的收益随时间成指数速度增长, 寻找与最优定常再调整策略的收益具有相同指数增长率的在线序贯投资组合是近年来投资组合研究的一个 热点. 首先提出了基于线性学习函数的在线投资组合策略, 其中线性函数的系数是一个与股票相对价格和收益有关的区间的中点. 用相对熵函数定义两个投资组合向量之 间的距离, 进一步证明了基于线性函数的在线投资组合策略是泛证券投资组合. 最后, 分别在两支股票和三支股票组成的多个投资组合上进行了数值计算, 并 与Cover等人提出的泛证券投资组合策略进行了比较. 结果表明这种基于线性学习函数的在线投资组合策略能获得更多的收益, 从而为投资者提供了新的 在线序贯投资组合决策的方法和依据, 具有重要的现实指导意义.

Universal portfolio based on on-line learning of linear function

The return of the best constant rebalanced portfolio(BCRP) has exponential growth rate with time.It is a hot topic to research on-line sequential investment strategy that has the same growth rate as BCRP.Based on the on-line learning of linear function,we firstly present a new on-line portfolio selection strategy,where the linear coefficient is the middle of an interval.And the interval is related to price relative and the return.Using the relative entropy as the distance function of two portfolios,we further prove that the new on-line portfolio is universal.Finally,take experiment on several portfolios that consisted of two stocks or three stocks,and compare the new strategy with Cover’s UP strategy.The results show that this new strategy can obtain better performance.Therefore,this paper provides a new method and basis for decision-making for on-line sequential investment,and thus has great practical significance.