Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market

TL;DR

This paper develops a rigorous sub- and super-solution framework to accurately analyze the asymptotic behavior of portfolio optimization strategies in complex multiscale stochastic markets with general utility functions.

Contribution

It extends previous asymptotic approximation methods to more general utility functions and dual timescale factors using a sub- and super-solution approach for rigorous accuracy validation.

Findings

Validated asymptotic approximations for general utilities and two-scale factors.

Constructed sub- and super-solutions to bound the value function.

Achieved precise error estimates for portfolio optimization in multiscale models.

Abstract

The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accurate analysis for cases with general utility functions and two timescale factors by constructing sub- and super-solutions to the fully nonlinear problem so that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.