[This article was first published on T. Moudiki's Webpage - R, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.Reimagining Equity Solvency Capital Requirement Approximation (one of my Master’s Thesis subjects): From Bilinear Interpolation to Probabilistic Machine LearningIn the world of insurance and financial risk management, calculating the Solvency Capital Requirement (SCR) for equity risk could be a computationally intensive task that can make or break real-time decision making. Traditional approaches rely on expensive Monte Carlo simulations that can take hours to complete, forcing practitioners to develop approximation schemes. Developing an approximation scheme was a project I tackled back in 2007-2009 for my Master’s Thesis in Actuarial Science (see references below).What I did back then 96 expensive ALIM simulations were run across four key variables: Minimum guaranteed rate (tmg): 1.75% to 6% Percentage of investments in stocks: 2% to 6.25% Latent capital gains on equities: 2% to 6.25% Profit sharing provisions (ppe): 3.5 to 10 Multi-stage interpolation strategy: I decomposed the problem into multiple 2D approximation grids, then combined cross-sections to reconstruct the full 4D surface. Validation through error analysis: Rigorous comparison between simulation results and approximations to ensure the method’s reliability.A Modern Probabilistic ApproachToday, I revisit this same challenge through the lens of probabilistic machine learning, and obtain functional expressions/approximations in R and Python. Fascinating how easy it may look now!This probabilistic approach offers several advantages: Built-in uncertainty quantification: Know not just the prediction, but how confident we should be Automatic feature learning: Let the model discover optimal representations FastOf course, having a functional probabilistic machine learning model, we can think of many ways to stress test (i.e obtain what-if analyses) these results, based on changes in one (or more) of the explanatory variablesReferences: Moudiki, T. (2012). Modélisation du SCR Equity. Institut des Actuaires. PDF ResearchGate version: https://www.researchgate.net/publication/395528539_memoire_moudiki_2012R version(scr_equity