求解log—最优组合投资问题的一个自适应算法及其理论分析

本文给出了一个求解log－最优组合投资问题的自适应算法，它是一个变型的随机逼近方法。该问题是一个约束优化问题，因此，采用基于约束流形的梯度上升方向替代常规梯度上升方向，在一些合理的假设下证明了算法的收敛性并进行了渐近稳定性分析。最后，本文将该算法应用于上海证券交易所提供的实际数据的log-最优组合投资问题求解，获得了理想的数值模拟结果。

An Adaptive Algorithm for log-optimal Portfolio and its Theoretical Analysis

In this paper, an effectively adaptive algorithm for solving log-optimal portfolio problem is proposed. It is a variant type of stochastic approximation algorithm. Since the problem considered here is a constrained optimization problem, the gradient ascent direction used conventionally is replaced by the steepest ascent tangent vector on the corresponding constraint manifold. Under some reasonable conditions, the convergence property of this algorithm is also demonstrated. Finally, this algorithm is applied to search optimal portfolio with real data of the Exchange Institute of Shanghai Security, the obtained numerical results are satisfactory.