Machine Learning Techniques in Nested Stochastic Simulation for Life Insurance

Machine Learning Techniques in Nested Stochastic Simulation for Life Insurance


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Solvency II, the harmonized European Directive for insurance and reinsurance companies [4], introduces new fundamental measures, such as the Probability Distribution Forecast (PDF) and the Solvency Capital Requirement (SCR), whose estimation involves a market-consistent evaluation of assets and liabilities. An expression in closed form of all components of assets and liabilities is unfeasible, due the complexity of their payoff. Numerical techniques such as Monte Carlo (MC) simulations are therefore used. In Solvency II evaluation framework, insurance undertakings must estimate the Net Asset Value (NAV) on a one-year time horizon. This value depends on the future Economic and Actuarial  scenario, and an estimation of its probability distribution _ the PDF _ requires nested Monte Carlo simulation. Nested MC method yields accurate results but it can present unacceptable computational costs [1]. One possible solution is Least Square Monte Carlo (LSMC), firstly developed for American-style derivatives, based on orthogonal polynomials [3]. We propose an alternative approach based on Machine Learning. In particular, the performance of Deep Learning Network (DLN) and Support Vector Regression (SVR), integrated with the Disar system - an asset-liability computational system for monitoring life insurance policies [2] - is investigated in terms of accuracy and robustness in the evaluation of PDF and SCR. The results are compared against the traditional LSMC methodology.


[1] Bauer, D., Reuss, A., Singer, D., (2012), “On the calculation of the solvency capital requirement based on nested simulations.” ASTIN bulletin: The Journal of the IAA , vol. 42(2), pp. 453-499.

[2] Castellani, G., Passalacqua, L., (2010), “Applications of distributed and parallel computing in the solvency II framework: the DISAR system” European Conference on Parallel Processing., p. 413-421.

[3] Longstaff, F.A., Schwartz, E.S.(2001), “Valuing american options by simulation: a simple leastsquares approach.” The review of financial studies, vol. 14(1), pp. 113-147.

[4] Solvency II, (2009) “Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of insurance and reinsurance.”

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