A STATISTICAL APPROXIMATION ALGORITHM OF THE OPTIMUM INVESTMENT STRATEGY

Let \barX=（X₁,…,X_m） be a random vector representing stock market price with probability distribution functionF（\barx）=F（x₁,…,x_m）, and let \barb=（b₁,…,b_m） be an investment strategy, where b_i≥0, ∑_ib_i=1. The W(\barX ; \barb)=\int \log \left(\Sigma_i b_i \cdot x_i\right) d F\left(x_1, \cdots, x_m\right) is said to be a doubling rate of （\barX, \barx）. A strategy b^* is satd to be optimumal on vector \barx （or distribution function F（\barx） if W\left(\barX ; \zeta^*\right)=\max \left\W(\barX ; \barb)\right., for all \left.\barb=\left(b_1, \cdots, b_m\right): b_i \geqslant 0, \Sigma_i b_i=1\right\.A core problem of the investment is to find the optimum strategy. The problem is considered in many papers under condition of the distribution function F（\barx） being known. In this paper, we give a statistical algorithm for the optimum strategy \barb^* in the case of m=2. and have proved that the estimation is a uniformly distributed statistics.