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Mean-field Libor market model and valuation of long term guarantees

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  • Florian Gach
  • Simon Hochgerner
  • Eva Kienbacher
  • Gabriel Schachinger

Abstract

Existence and uniqueness of solutions to the multi-dimensional mean-field Libor market model (introduced by [7]) is shown. This is used as the basis for a numerical asset-liability management (ALM) model capable of calculating future discretionary benefits in accordance with Solvency~II regulation. This ALM model is complimented with aggregated life insurance data to perform a realistic numerical study. This yields numerical evidence for heuristic assumptions which allow to derive estimators of lower and upper bounds for future discretionary benefits. These estimators are applied to publicly available life insurance data.

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  • Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2310.09022
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    References listed on IDEAS

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    1. Engsner, Hampus & Lindholm, Mathias & Lindskog, Filip, 2017. "Insurance valuation: A computable multi-period cost-of-capital approach," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 250-264.
    2. Hansjoerg Albrecher & Daniel Bauer & Paul Embrechts & Damir Filipović & Pablo Koch-Medina & Ralf Korn & Stéphane Loisel & Antoon Pelsser & Frank Schiller & Hato Schmeiser & Joël Wagner, 2017. "Asset-Liability Management for Long-Term Insurance Business," Swiss Finance Institute Research Paper Series 17-69, Swiss Finance Institute, revised Jan 2018.
    3. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    4. Anna Rita Bacinello & An Chen & Thorsten Sehner & Pietro Millossovich, 2021. "On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk," Risks, MDPI, vol. 9(1), pages 1-18, January.
    5. Gach, Florian & Hochgerner, Simon, 2022. "Estimation Of Future Discretionary Benefits In Traditional Life Insurance," ASTIN Bulletin, Cambridge University Press, vol. 52(3), pages 835-876, September.
    6. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    7. Simon Hochgerner & Florian Gach, 2018. "Analytical Validation Formulas for Best Estimate Calculation in Traditional Life Insurance," Papers 1802.07009, arXiv.org, revised Jul 2019.
    8. Gerhold, Stefan, 2011. "Moment explosion in the LIBOR market model," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 560-562, May.
    9. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
    10. Diana Dorobantu & Yahia Salhi & Pierre-E. Thérond, 2020. "Modelling Net Carrying Amount of Shares for Market Consistent Valuation of Life Insurance Liabilities," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 711-745, June.
    11. Nicole El Karoui & Stéphane Loisel & Jean-Luc Prigent & Julien Vedani, 2017. "Market inconsistencies of the market-consistent European life insurance economic valuations: pitfalls and practical solutions," Post-Print hal-01242023, HAL.
    12. Florian Gach & Simon Hochgerner, 2021. "Estimation of future discretionary benefits in traditional life insurance," Papers 2101.06077, arXiv.org, revised Jul 2022.
    13. Sheldon, T. J. & Smith, A. D., 2004. "Market Consistent Valuation of Life Assurance Business," British Actuarial Journal, Cambridge University Press, vol. 10(3), pages 543-605, August.
    14. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    15. Łukasz Delong, 2011. "Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities," Bank i Kredyt, Narodowy Bank Polski, vol. 42(1), pages 49-78.
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