[Paper Review] Risk management with machine-learning-based algorithms

Simon F'ecamp, Joseph Mikael+1 more|arXiv (Cornell University)|Feb 14, 2019

Big Data and Business Intelligence5 citations

TL;DR

This paper proposes a deep learning-based global optimization algorithm using neural networks and LSTM architectures to solve discrete-time hedging problems in incomplete markets with transaction costs, illiquidity, and non-tradable risk factors. The method efficiently computes optimal hedging strategies across multiple risk criteria and enables single-phase training to estimate the full Pareto frontier between risk and transaction costs, outperforming classical stochastic control methods in speed and flexibility while maintaining high accuracy in high-dimensional settings.

ABSTRACT

We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies are compared to classical stochastic control techniques on several payoffs using a variance criterion. One of the proposed algorithm is flexible enough to be used with several existing risk criteria. We furthermore propose a new moment-based risk criteria.

Motivation & Objective

• To address the limitations of classical stochastic control methods in high-dimensional, incomplete markets with transaction costs and illiquidity.
• To develop a flexible machine learning framework that supports arbitrary risk criteria beyond mean squared error.
• To enable efficient computation of the full Pareto frontier between risk and transaction costs in a single training phase.
• To compare global and local neural network architectures for hedging under variance and non-symmetric loss functions.
• To demonstrate the feasibility and superiority of deep learning in solving complex, real-world hedging problems previously intractable with dynamic programming.

Proposed method

• Uses a global deep neural network to solve a single optimization problem that minimizes a user-defined risk criterion over the entire hedging horizon.
• Employs an LSTM-based architecture to model non-Markovian dynamics and handle time-dependent state dependencies.
• Introduces a multi-objective training strategy by including a hyperparameter α in the network input, randomly sampled from U(0,1), to jointly optimize for risk (variance) and transaction cost.
• Applies mini-batch stochastic gradient descent with a Sobol quasi-random generator for α to improve convergence and coverage of the Pareto frontier.
• Defines a composite loss function: dα(XΔ, g(ST)) = (1−α)E[ YT ] + α√E[(XT −g(ST))²], which balances transaction costs and hedging error.
• Validates performance against a reference dynamic programming algorithm from Warin (2019) using high-performance computing.

Experimental results

Research questions

• RQ1 Can deep learning-based global optimization outperform classical stochastic control methods in high-dimensional hedging problems with transaction costs and illiquidity?
• RQ2 How does the choice of risk criterion—especially non-symmetric or moment-based—impact the distribution of the hedged portfolio’s P&L?
• RQ3 Can a single neural network training phase produce a full Pareto frontier between risk and transaction cost, eliminating the need for multiple retraining runs?
• RQ4 What is the relative performance of global versus local optimization architectures in deep learning-based hedging?
• RQ5 To what extent can LSTM-based networks handle non-Markovian underlying processes in incomplete market hedging?

Key findings

• The global deep learning algorithm significantly outperforms local optimization approaches in terms of both accuracy and computational efficiency, avoiding local minima common in iterative methods.
• The global approach achieves results comparable to high-performance dynamic programming methods in low dimensions but scales effectively to higher dimensions where classical methods fail.
• Non-symmetric loss functions (e.g., L2/L4 and asymmetrical loss) reduce extreme losses and shift portfolio distribution toward gains, at the cost of slightly higher average losses.
• By training with randomly sampled α values, the method produces a complete Pareto frontier between risk and transaction cost in a single training run, enabling fast inference and sensitivity analysis.
• The use of LSTM in the global network allows for flexible modeling of non-Markovian dynamics, expanding applicability beyond standard Markovian assumptions.
• The algorithm successfully handles complex hedging problems involving illiquidity, non-tradable risk factors, and proportional transaction costs, demonstrating robustness and practical relevance.