Portfolio Growth Rate and Ergodic Capacity of Fading Channels

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.