Cover's Algorithm Modified for Nonparametric Estimation of a Log-Optimal Portfolio Selection Function

Abstract

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 observed vectors (fixed d ∈ ℕ) on the basis of an observed training sequence of vectors. Under a boundedness and a mild -mixing condition, a strong consistency result is established.