Optimal Investment Portfolio Optimization under Stochastic Volatility with Receding Horizon Control

Project Abstract

We propose a rigorous framework for optimizing investment portfolios under stochastic volatility using receding horizon control (RHC) to manage dynamic risk and return trade-offs in realistic market environments. The study integrates stochastic volatility models, such as Heston-type dynamics, with a model predictive control approach to determine adaptive portfolio weights over a finite prediction horizon. We develop a multi-period stochastic optimization problem that maximizes expected utility or minimizes a risk-adjusted cost function subject to budget, no-arbitrage, and transaction cost constraints. The core contribution lies in deriving tractable reformulations that leverage affine and approximate dynamic programming techniques to handle the nonlinearity and path-dependence intrinsic to volatility-driven return processes. We introduce a robust objective that incorporates risk measures (e.g., conditional value-at-risk, entropic risk) and liquidity constraints, ensuring resilience to model misspecification and market microstructure frictions. The methodology combines stochastic control with contemporary numerical methods, including scenario-based rollouts, sample-average approximations, and convexification via penalty methods to enable scalable computation for high-dimensional portfolios. We perform a comprehensive comparative analysis against benchmarks using both synthetic data generated from stochastic volatility models and real-world equity and derivative price series. The results demonstrate that the RHC framework achieves superior risk-adjusted performance, reduced drawdowns, and enhanced tail behavior control relative to static and myopic strategies, particularly in regimes of elevated volatility and abrupt regime shifts. We examine the sensitivity of optimal policy trajectories to key parameters such as the volatility of volatility, correlation between asset returns and volatility shocks, prediction horizon length, and transaction costs. The study also investigates the impact of different risk aversion profiles and utility specifications on portfolio behavior, revealing conditions under which diversification benefits are maintained even during volatility surges. Additionally, we address practical considerations for implementation, including estimation of latent volatility factors, calibration of the Heston-type dynamics, and real-time updating of optimization problems within out-of-sample trading simulations. The findings provide theoretical and empirical support for deploying receding horizon control in portfolio management to accommodate non-Gaussian return characteristics, stochastic volatility persistence, and market frictions, thereby offering a viable pathway to improved performance, enhanced risk containment, and adaptive decision-making in modern financial markets. The work closes with recommendations for practitioners and avenues for future research, such as extending the framework to multi-asset derivatives portfolios, incorporating learning-based model updates, and exploring alternative risk measures within the RHC paradigm.

Project Overview

What This Project Is About

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A plain-language overview of how investors can choose portfolios when market volatility changes randomly over time. The project blends ideas from finance with simple models that capture how uncertainty in asset prices can shift in unpredictable ways, and it uses a planning method that looks ahead a few steps to make better current choices.

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The Problem It Addresses

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Traditional portfolio methods often assume constant risk and predictable returns. In real markets, volatility swings can hurt returns and increase risk unexpectedly. This project investigates how to make investment decisions that adapt to changing risk, aiming to improve long-term performance while controlling downside risk.

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Objectives of the Project

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1. Explain the key ideas behind portfolio optimization and stochastic volatility in simple terms.
2. Develop a basic model that allows for changing volatility and plan over a short horizon.
3. Demonstrate how the receding horizon approach helps adapt decisions as market data evolves.
4. Evaluate the model with small, accessible datasets to illustrate potential gains and trade-offs.

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What You Will Do Step by Step

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1. Learn the core concepts with non-technical explanations.

2. Build a straightforward mathematical model that includes changing risk.

3. Implement a simple receding horizon control scheme to update decisions.

4. Run basic tests using historical data and simulate outcomes.

5. Analyze results with clear visuals and discuss practical limits.

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Expected Outcome

Clear, easy-to-follow guidelines for choosing portfolios under shifting volatility, with a demonstration of how short-term planning can improve risk-adjusted returns. The project should provide intuition, a runnable example, and notes on potential real-world applications and limitations.