Portfolio Growth Rate and Ergodic Capacity of Fading Channels

TL;DR

This paper establishes a connection between portfolio growth rates and the capacity of fading MIMO channels, providing new insights into stochastic ordering, side information benefits, and statistical testing in investment models.

Contribution

It introduces a novel relationship between financial portfolio growth and channel capacity, along with bounds on side information gains and a new statistical test for side information usefulness.

Findings

Relationship between portfolio growth rate and channel capacity established

Bounds on growth-rate gains due to side information derived

A new statistical test for side information usefulness proposed

Abstract

A relationship between the growth-rate of logoptimal portfolios and capacity of fading single-input multiple output (SIMO) channels are established. Using this relation, stock vector stochastic processes that model the investment environments are stochastically ordered using different criteria. The presence of side information (SI) is considered, and a bound on the gains in the growth-rate due to SI is derived along with data processing inequality and convexity properties. A statistical test on the usefulness of SI that does not require the computation of the optimal portfolio vector in the presence of SI is introduced and its several variants are discussed.