Transformers-based least square Monte Carlo for solvency calculation in life insurance

The Solvency Capital Requirement (SCR), mandated by Solvency II, represents the capital insurers must hold to ensure solvency, calculated as the Value-at-Risk of the Net Asset Value at a 99.5% confidence level over a one-year period. While Nested Monte Carlo simulations are the gold standard for SCR calculation, they are highly resource-intensive. The Least Squares Monte Carlo (LSMC) method provides a more efficient alternative but faces challenges with high-dimensional data due to the curse of dimensionality. We introduce a novel extension of LSMC, incorporating advanced deep learning models, specifically Transformer models, which enhance traditional machine learning methods. This approach significantly improves the accuracy of approximating the complex relationship between insurance liabilities and risk factors, leading to a more accurate SCR calculation. Our extensive experiments on two insurance portfolios demonstrate the effectiveness of this transformer-based LSMC approach. Additionally, we show that Shapley values can be applied to achieve model explainability, which is crucial for regulatory compliance and for fostering the adoption of deep learning in the highly regulated insurance sector.