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

2025-10-24

AI Summary

This paper addresses dynamic portfolio allocation under stochastic volatility with both exogenous proportional transaction costs and endogenous liquidity risk. Methodologically, it formulates the first five-dimensional nonlinear Hamilton–Jacobi–Bellman (HJB) model integrating both cost components; calibrates an S-shaped utility function via option-implied methods; handles its non-concavity through concave envelope transformation; and develops a novel deep learning–based policy iteration algorithm for efficient high-dimensional HJB solution. Results show significant interaction between exogenous and endogenous trading costs; stochastic volatility dynamics substantially reduce leverage and amplify rebalancing inertia. The derived optimal strategy exhibits markedly improved alignment with empirical investor behavior—demonstrating strong explanatory power and superior in-sample and out-of-sample fit relative to benchmark models.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
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Application Category

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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.

Problem

• Portfolio selection with stochastic volatility and transaction costs
• Modeling endogenous liquidity risk and exogenous costs
• Solving five-dimensional HJB equation via deep learning

Innovation

• Two-factor stochastic volatility model with mean-reversion
• Option-implied S-shaped utility function transformation
• Deep learning policy iteration for HJB equation solution