Portfolio selection with exogenous and endogenous transaction costs under a two-factor stochastic volatility model

TL;DR

This paper develops a sophisticated model for portfolio optimization considering complex transaction costs and stochastic volatility, employing deep learning for numerical solutions and analyzing their impact on investment strategies.

Contribution

It introduces a novel approach combining stochastic volatility, endogenous and exogenous transaction costs, and deep learning to solve a high-dimensional nonlinear control problem.

Findings

Transaction costs significantly influence optimal investment strategies.

Stochastic volatility affects the sensitivity of the optimal policy.

Deep learning effectively solves high-dimensional HJB equations.

Abstract

In this paper, we investigate a portfolio selection problem with transaction costs under a two-factor stochastic volatility structure, where volatility follows a mean-reverting process with a stochastic mean-reversion level. The model incorporates both proportional exogenous transaction costs and endogenous costs modeled by a stochastic liquidity risk process. Using an option-implied approach, we extract an S-shaped utility function that reflects investor behavior and apply its concave envelope transformation to handle the non-concavity. The resulting problem reduces to solving a five-dimensional nonlinear Hamilton-Jacobi-Bellman equation. We employ a deep learning-based policy iteration scheme to numerically compute the value function and the optimal policy. Numerical experiments are conducted to analyze how both types of transaction costs and stochastic volatility affect optimal investment decisions.