Deep Hedging en finance et assurance pour la couverture en marché incomplet des produits complexe de type Variables annuités ou Universal Life

Details

Supervisors

Barbarin, Jérôme

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enModern life insurance products, such as Variable Annuities or Universal Life contracts, are characterized by high complexity, resulting from the combination of often path-dependent financial guarantees, biometric risks, and implied options. This hybrid structure makes them practically unreplicable in incomplete markets, where traditional hedging approaches, such as delta hedging, quickly reveal their limitations. In this context, this thesis proposes an innovative approach based on deep hedging, which uses neural network architectures, particularly Feedforward Neural Networks (FFNNs) and Long Short-Term Memory (LSTMs), to directly learn optimal hedging strategies from market simulations. The framework relies on a stochastic volatility Heston model, enhanced by the introduction of transaction costs and by modeling under the real probability measure, via Monte Carlo simulations, enabling the capture of realistic market dynamics. Unlike a complete market, where any contingent asset can be perfectly replicated, the goal here is not exact replication, but rather the construction of a dynamic asset portfolio that minimizes the hedging error between assets and liabilities. This optimization relies on asymmetric and convex cost functions, such as Conditional Value-at-Risk (CVaR) and entropic risk, reflecting insurers' economic preferences to limit extreme losses while preserving profit potential. Empirical results highlight remarkable performance: deep hedging enables a significant reduction in the profit and loss (P&L) error, even in the most adverse 1% of market scenarios. Furthermore, the learned strategies clearly outperform traditional approaches, particularly delta hedging, in terms of robustness, economic efficiency, and success rate. Sensitivity analyses and robustness tests confirm the stability and operational viability of the proposed approach for risk management in life insurance.