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

Author

Walk, Harro

Author_Institution

Fachbereich Math., Univ. Stuttgart, Stuttgart, Germany

Volume

59

Issue

8

fYear

2013

fDate

Aug. 2013

Firstpage

4771

Lastpage

4780

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.

Keywords

approximation theory; estimation theory; investment; iterative methods; regression analysis; stochastic processes; stock markets; vectors; cover algorithm; distribution function; expected log investment return maximization; iterative estimation; iterative portfolio choice; log-optimal portfolio selection function; nonparametric regression estimation the algorithm; observed training vector sequence; stationary ergodic sequence; stochastic approximation algorithm; stock market vectors; unknown distribution; Approximation algorithms; Approximation methods; Convergence; Estimation; Investment; Portfolios; Vectors; $alpha $-mixing; Cover\´s algorithm; kernel regression estimation; log-optimal portfolio selection function; partitions; stationary ergodic training sequence; stochastic approximation; strong consistency;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2013.2257914

Filename

6529190