Cover's Algorithm Modified for Nonparametric Estimation of a Log-Optimal Portfolio Selection Function
Cover's algorithm yields an iterative portfolio choice for maximizing expected log investment return where the distribution function of the stock market vector is known. In the case that the stock market vectors form a stationary ergodic sequence with unknown distribution, by stochastic approximation and nonparametric regression estimation the algorithm is modified for iterative estimation of a log-optimal portfolio selection function of the last d observed vectors (fixed d is an element of N) on the basis of an observed training sequence of vectors. Under a boundedness and a mild alpha-mixing condition, a strong consistency result is established.
cover's algorithm log-optimal portfolio selection function stochastic approximation alpha-mixing strong consistency kernel regression estimation partitions stationary ergodic training sequence