Explainable Least Square Monte Carlo for Solvency Calculation in Life Insurance

The Solvency II directive mandates insurance undertakings to maintain eligible own funds covering the Solvency Capital Requirement (SCR). The SCR is defined as the Value-at-Risk of the Net Asset Value probability distribution at a 99.5\% confidence level over a one-year period. Estimating the SCR involves nested simulations, incurring prohibitive computational costs. While machine and deep learning methods exhibit accuracy, their lack of explainability limits the adoption in the highly regulated insurance sector. This paper introduces an extension of the Least Square Monte Carlo  method based on recent advances in explainable deep learning. The proposed approach allows for an accurate estimation of the SCR without compromising model explainability. It allows for deriving some interesting insights into the impact of risk factors on the value of the insurance liabilities. Numerical experiments performed on two realistic insurance portfolios validate our proposal. Additionally, we illustrate that the ElasticNet regularisation can be applied to further enhance the model's performance.