Portfolio Choice with Stochastic Volatility and Transaction Costs

Summary

The paper studies optimal portfolio selection when asset volatility has two stochastic factors: a mean-reverting component and a stochastic mean-reversion level. Trading incurs proportional exogenous costs as well as endogenous costs linked to a stochastic liquidity-risk process. Investor preferences are represented by an S-shaped utility function inferred through an option-implied approach; a concave-envelope transformation is used to address its non-concavity.

The transformed problem is expressed as a five-dimensional nonlinear Hamilton-Jacobi-Bellman equation. The authors use deep-learning-based policy iteration to calculate the value function and optimal investment policy, then run numerical experiments examining how transaction costs and stochastic volatility influence investment choices. The excerpt describes the modeling and computational approach but gives no specific policy findings, market calibration, or empirical validation, so its conclusions are limited to numerical analysis under the stated model.

Key ideas

• The volatility model includes both a mean-reverting factor and a stochastic mean-reversion level.
• The framework combines proportional trading costs with liquidity-driven endogenous costs.
• An option-implied S-shaped utility is transformed through its concave envelope.
• A deep learning policy-iteration method solves the resulting nonlinear HJB problem numerically.

Tags

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


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









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.

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