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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.
The revenue generated by the optimal constant readjustment strategy grows at an exponential rate over time and finding an online sequential portfolio with the same exponential growth rate as the return to the optimal constant reallocate strategy is a hot topic in the portfolio research in recent years. The online portfolio strategy based on the linear learning function, in which the coefficient of the linear function is the midpoint of a range related to the relative price and return of the stock, defines the distance between the two portfolio vectors using the relative entropy function, The online portfolio strategy of linear function is pan-securities portfolio.Finally, numerical calculation is carried out on several portfolios composed of two stocks and three stocks, respectively, and carried out with the pan-portfolio investment strategy proposed by Cover et al. The results show that the online portfolio strategy based on linear learning function can get more benefits, which provides investors with a new method and basis for decision-making of online sequential portfolio, which has important practical significance.