On the possibility of optimal investment

TL;DR

This paper examines the practical limitations of optimal investment strategies in risky assets, highlighting challenges posed by real data, transaction costs, and asset correlations, which hinder the implementation of theoretically optimal methods.

Contribution

It extends existing theoretical models by incorporating real data, transaction costs, and asset correlations to evaluate the feasibility of optimal investment strategies.

Findings

Optimal strategies are rarely feasible with real data.

Transaction costs significantly limit strategy applicability.

Correlations in asset prices complicate the optimization process.

Abstract

We analyze the theory of optimal investment in risky assets, developed recently by Marsili, Maslov and Zhang [Physica A 253 (1998) 403]. When the real data are used instead of abstract stochastic process, it appears that a non-trivial investment strategy is rarely possible. We show that non-zero transaction costs make the applicability of the method even more difficult. We generalize the method in order to take into account possible correlations in the asset price.