IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp85-103.html
   My bibliography  Save this article

Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach

Author

Listed:
  • Lin, X. Sheldon
  • Yang, Shuai

Abstract

The nested-simulation is commonly used for calculating the predictive distribution of the total variable annuity (VA) liabilities of large VA portfolios. Due to the large numbers of policies, inner-loops and outer-loops, running the nested-simulation for a large VA portfolio is extremely time consuming and often prohibitive. In this paper, the use of surrogate models is incorporated into the nested-simulation algorithm so that the relationship between the inputs and the outputs of a simulation model is approximated by various statistical models. As a result, the nested-simulation algorithm can be run with much smaller numbers of different inputs. Specifically, a spline regression model is used to reduce the number of outer-loops and a model-assisted finite population estimation framework is adapted to reduce the number of policies in use for the nested-simulation. From simulation studies, our proposed algorithm is able to accurately approximate the predictive distribution of the total VA liability at a significantly reduced running time.

Suggested Citation

  • Lin, X. Sheldon & Yang, Shuai, 2020. "Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 85-103.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:85-103
    DOI: 10.1016/j.insmatheco.2020.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300020
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.01.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Seyed Amir Hejazi & Kenneth R. Jackson, 2016. "A Neural Network Approach to Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1606.07831, arXiv.org.
    2. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    3. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    4. Hejazi, Seyed Amir & Jackson, Kenneth R., 2016. "A neural network approach to efficient valuation of large portfolios of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 169-181.
    5. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    6. 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.
    7. 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.
    8. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    9. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    10. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    11. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    12. Lin, X. Sheldon & Yang, Shuai, 2020. "Efficient Dynamic Hedging For Large Variable Annuity Portfolios With Multiple Underlying Assets," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 913-957, September.
    13. Bauer, Daniel & Reuss, Andreas & Singer, Daniela, 2012. "On the Calculation of the Solvency Capital Requirement Based on Nested Simulations," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 453-499, November.
    14. Desislava Nedyalkova & Yves Tillé, 2008. "Optimal sampling and estimation strategies under the linear model," Biometrika, Biometrika Trust, vol. 95(3), pages 521-537.
    15. Guojun Gan & Emiliano A. Valdez, 2018. "Regression Modeling for the Valuation of Large Variable Annuity Portfolios," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(1), pages 40-54, January.
    16. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Areski Cousin & Ying Jiao & Christian y Robert & Olivier David Zerbib, 2021. "Optimal asset allocation subject to withdrawal risk and solvency constraints," Working Papers hal-03244380, HAL.
    2. Gweon, Hyukjun & Li, Shu, 2021. "Batch mode active learning framework and its application on valuing large variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 105-115.
    3. Jiang, Ruihong & Saunders, David & Weng, Chengguo, 2023. "Two-phase selection of representative contracts for valuation of large variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 293-309.
    4. Gijs Mast & Xiaoyu Shen & Fang Fang, 2023. "Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion," Papers 2311.12575, arXiv.org.
    5. Wing Fung Chong & Haoen Cui & Yuxuan Li, 2021. "Pseudo-Model-Free Hedging for Variable Annuities via Deep Reinforcement Learning," Papers 2107.03340, arXiv.org, revised Oct 2022.
    6. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2022. "Effective experience rating for large insurance portfolios via surrogate modeling," Papers 2211.06568, arXiv.org, revised Jun 2024.
    7. Dang, Ou & Feng, Mingbin & Hardy, Mary R., 2023. "Two-stage nested simulation of tail risk measurement: A likelihood ratio approach," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 1-24.
    8. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
    9. Jeong, Himchan, 2024. "Tweedie multivariate semi-parametric credibility with the exchangeable correlation," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 13-21.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiang, Ruihong & Saunders, David & Weng, Chengguo, 2023. "Two-phase selection of representative contracts for valuation of large variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 293-309.
    2. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    3. Seyed Amir Hejazi & Kenneth R. Jackson, 2016. "Efficient Valuation of SCR via a Neural Network Approach," Papers 1610.01946, arXiv.org.
    4. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    5. Guojun Gan & Emiliano A. Valdez, 2018. "Nested Stochastic Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets," Data, MDPI, vol. 3(3), pages 1-21, September.
    6. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    7. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
    8. Massimo Costabile & Fabio Viviano, 2021. "Modeling the Future Value Distribution of a Life Insurance Portfolio," Risks, MDPI, vol. 9(10), pages 1-17, October.
    9. Gan Guojun & Valdez Emiliano A., 2017. "Valuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets," Dependence Modeling, De Gruyter, vol. 5(1), pages 354-374, December.
    10. Wing Fung Chong & Haoen Cui & Yuxuan Li, 2021. "Pseudo-Model-Free Hedging for Variable Annuities via Deep Reinforcement Learning," Papers 2107.03340, arXiv.org, revised Oct 2022.
    11. Xu, Wei & Chen, Yuehuan & Coleman, Conrad & Coleman, Thomas F., 2018. "Moment matching machine learning methods for risk management of large variable annuity portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 1-20.
    12. Seyed Amir Hejazi & Kenneth R. Jackson & Guojun Gan, 2017. "A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1701.04134, arXiv.org.
    13. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    14. Nguyen, Hang & Sherris, Michael & Villegas, Andrés M. & Ziveyi, Jonathan, 2024. "Scenario selection with LASSO regression for the valuation of variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 27-43.
    15. Guojun Gan, 2018. "Valuation of Large Variable Annuity Portfolios Using Linear Models with Interactions," Risks, MDPI, vol. 6(3), pages 1-19, July.
    16. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    17. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    18. Seyed Amir Hejazi & Kenneth R. Jackson, 2016. "A Neural Network Approach to Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1606.07831, arXiv.org.
    19. Gan, Guojun & Valdez, Emiliano A., 2017. "Modeling partial Greeks of variable annuities with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 118-134.
    20. Hejazi, Seyed Amir & Jackson, Kenneth R., 2016. "A neural network approach to efficient valuation of large portfolios of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 169-181.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:85-103. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.