Long time asymptotics for optimal investment

TL;DR

This paper surveys long-term portfolio optimization, analyzing asymptotic behaviors of growth objectives using large deviations and duality methods, with explicit solutions in linear factor models.

Contribution

It provides a comprehensive review of asymptotic portfolio optimization problems and derives explicit solutions in linear factor models.

Findings

Asymptotic behavior characterized by large deviations principles.

Duality methods effectively solve ergodic risk-sensitive problems.

Explicit solutions obtained for linear factor models.

Abstract

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control pro\-blems, that we solve by duality method leading to ergodic risk-sensitive portfolio optimization problems. Special emphasis is placed on linear factor models where explicit solutions are obtained.