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A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies

Author

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  • Anne-Sophie Krah

    (Department of Mathematics, TU Kaiserslautern, Erwin Schrödinger Strasse, Geb. 48, 67653 Kaiserslautern, Germany)

  • Zoran Nikolić

    (Mathematical Institute, University Cologne, Weyertal 86-90, 50931 Cologne, Germany)

  • Ralf Korn

    (Department of Mathematics, TU Kaiserslautern, Erwin Schrödinger Strasse, Geb. 48, 67653 Kaiserslautern, Germany
    Department Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

Abstract

The Solvency II directive asks insurance companies to derive their solvency capital requirement from the full loss distribution over the coming year. While this is in general computationally infeasible in the life insurance business, an application of the Least-Squares Monte Carlo (LSMC) method offers a possibility to overcome this computational challenge. We outline in detail the challenges a life insurer faces, the theoretical basis of the LSMC method and the necessary steps on the way to a reliable proxy modeling in the life insurance business. Further, we illustrate the advantages of the LSMC approach via presenting (slightly disguised) real-world applications.

Suggested Citation

  • Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2018. "A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 6(2), pages 1-26, June.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:62-:d:151752
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    References listed on IDEAS

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    1. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    2. Seyed Amir Hejazi & Kenneth R. Jackson, 2016. "Efficient Valuation of SCR via a Neural Network Approach," Papers 1610.01946, arXiv.org.
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mark Kiermayer & Christian Wei{ss}, 2019. "Grouping of Contracts in Insurance using Neural Networks," Papers 1912.09964, arXiv.org.
    2. Aur'elien Alfonsi & Adel Cherchali & Jose Arturo Infante Acevedo, 2020. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Papers 2010.12651, arXiv.org, revised Apr 2021.
    3. Massimo Costabile & Fabio Viviano, 2020. "Testing the Least-Squares Monte Carlo Method for the Evaluation of Capital Requirements in Life Insurance," Risks, MDPI, vol. 8(2), pages 1-13, May.
    4. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org.
    5. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
    6. Alfonsi, Aurélien & Cherchali, Adel & Infante Acevedo, Jose Arturo, 2021. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 234-260.
    7. Weiß Christian & Nikolić Zoran, 2019. "An aspect of optimal regression design for LSMC," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 283-290, December.
    8. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 8(1), pages 1-79, February.
    9. Aur'elien Alfonsi & Bernard Lapeyre & J'er^ome Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Papers 2209.04153, arXiv.org, revised May 2023.
    10. Claus Baumgart & Johannes Krebs & Robert Lempertseder & Oliver Pfaffel, 2019. "Quantifying Life Insurance Risk using Least-Squares Monte Carlo," Papers 1910.03951, arXiv.org.
    11. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Post-Print hal-03770051, HAL.
    12. Lu Xiong & Jiyao Luo & Hanna Vise & Madison White, 2023. "Distributed Least-Squares Monte Carlo for American Option Pricing," Risks, MDPI, vol. 11(8), pages 1-16, August.
    13. Massimo Costabile & Fabio Viviano, 2021. "Modeling the Future Value Distribution of a Life Insurance Portfolio," Risks, MDPI, vol. 9(10), pages 1-17, October.
    14. Jo~ao F. Doriguello & Alessandro Luongo & Jinge Bao & Patrick Rebentrost & Miklos Santha, 2021. "Quantum algorithm for stochastic optimal stopping problems with applications in finance," Papers 2111.15332, arXiv.org, revised Jul 2023.
    15. Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.
    16. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Least-Squares Monte Carlo for Proxy Modeling in Life Insurance: Neural Networks," Risks, MDPI, vol. 8(4), pages 1-21, November.
    17. Anne-Sophie Krah & Zoran Nikoli'c & Ralf Korn, 2019. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Papers 1909.02182, arXiv.org.
    18. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Working Papers hal-03770051, HAL.

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