Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T15:36:02.487Z Has data issue: false hasContentIssue false

ESTIMATION OF FUTURE DISCRETIONARY BENEFITS IN TRADITIONAL LIFE INSURANCE

Published online by Cambridge University Press:  06 September 2022

Florian Gach
Affiliation:
Austrian Financial Market Authority (FMA) Otto-Wagner Platz 5, A-1090 Vienna, Austria E-mail: [email protected]
Simon Hochgerner*
Affiliation:
Austrian Financial Market Authority (FMA) Otto-Wagner Platz 5, A-1090 Vienna, Austria E-mail: [email protected]

Abstract

In the context of life insurance with profit participation, the future discretionary benefits (FDB), which are a central item for Solvency II reporting, are generally calculated by computationally expensive Monte Carlo algorithms. We derive analytic formulas to estimate lower and upper bounds for the FDB. This yields an estimation interval for the FDB, and the average of lower and upper bound is a simple estimator. These formulae are designed for real world applications, and we compare the results to publicly available reporting data.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Disclaimer. The opinions expressed in this article are those of the authors and do not necessarily reflect the official position of the Austrian Financial Market Authority.

References

Albrecher, H., Bauer, D., Embrechts, P. et al. (2018) Asset-liability management for long-term insurance business. European Actuarial Journal, 8, 925. https://doi.org/10.1007/s13385-018-0167-5 CrossRefGoogle Scholar
Allianz Lebensversicherungs-AG, (2017a) Geschäftsbericht. https://www.allianzdeu-tschland.de/geschaeftsberichte-der-allianz-deutschland-ag. Accessed 4 Sep 2020.Google Scholar
Allianz Lebensversicherungs-AG, (2017b) Bericht Über Solvabilität und Finanzlage. https://www.allianzdeutschland.de/berichte-ueber-solvabilitaet-und-finanzlage. Accessed 4 Sep 2020.Google Scholar
Allianz Lebensversicherungs-AG, (2018a) Geschäftsbericht. https://www.allianzdeu-tschland.de/geschaeftsberichte-der-allianz-deutschland-ag. Accessed 4 Sep 2020.Google Scholar
Allianz Lebensversicherungs-AG, (2019a) Geschäftsbericht. https://www.allianzdeu-tschland.de/geschaeftsberichte-der-allianz-deutschland-ag. Accessed 4 Sep 2020.Google Scholar
Allianz Lebensversicherungs-AG, (2018b) Bericht Über Solvabilität und Finanzlage. https://www.allianzdeutschland.de/berichte-ueber-solvabilitaet-und-finanzlage. Accessed 4 Sep 2020.Google Scholar
Allianz Lebensversicherungs-AG, (2019b) Bericht Über Solvabilität und Finanzlage. https://www.allianzdeutschland.de/berichte-ueber-solvabilitaet-und-finanzlage. Accessed 4 Sep 2020.Google Scholar
Bacinello, A.R., Sehner, T. and Millossovich, P. (2021) On the market-consistent valuation of participating life insurance heterogeneous contracts under longevity risk. Risks, 9(1), 20. https://doi.org/10.3390/risks9010020 CrossRefGoogle Scholar
Black, F. (1976) The pricing of commodity contracts. Journal of Financial Economics, 3, 167179. https://doi.org/10.1016/0304-405X(76)90024-6 CrossRefGoogle Scholar
Brigo, D. and Mercurio, F. (2006) Interest Rate Models – Theory and Practice. Berlin, Heidelberg: Springer.Google Scholar
Bundesanstalt für Finanzdienstleistungsaufsicht, (2019) Statistik der BaFin - Erstversicherungsunternehmen - Lebensversicherung. https://www.bafin.de/SharedDocs/Downloads/DE/Statistik/Erstversicherer/dl_st_19_erstvu_lv_va_xls.xlsm?__blob=publicationFilev=2 Google Scholar
Bundesgesetz Über den Betrieb und die Beaufsichtigung der Vertragsversicherung (Versicherungsaufsichtsgesetz 2016 – VAG 2016).Google Scholar
Bundesministerium der Finanzen (BMF). Verordnung Über die Mindestbeitragsrückerstattung in der Lebensversicherung.Google Scholar
Commission Delegated Regulation (EU) 2015/35 of 10 October 2014 supplementing Directive 2009/138/EC of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II).Google Scholar
Commission Implementing Regulation (EU) 2015/2450 of 2 December 2015 laying down implementing technical standards with regard to the templates for the submission of information to the supervisory authorities according to Directive 2009/138/EC of the European Parliament and of the Council.Google Scholar
Delong, L. (2011) Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities. Bank i Kredyt, Narodowy Bank Polski, 42(1), 4978.Google Scholar
Dhaene, J., Stassen, B., Barigou, K., Linders, D. and Chen, Z. (2017) Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency. Insurance: Mathematics and Economics, 76, 1427. https://doi.org/10.1016/j.insmatheco.2017.06.003.Google Scholar
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 (Solvency II).Google Scholar
Dorobantu, D., Salhi, Y. and Therond, P.-E. (2020) Modelling net carrying amount of shares for market consistent valuation of life insurance liabilities. Methodology and Computing in Applied Probability, 22, 711745. https://doi.org/10.1007/s11009-019-09729-1 CrossRefGoogle Scholar
Engsner, H., Lindholm, M. and Lindskog, F. (2017) Insurance valuation: A computable multi-period cost-of-capital approach. Insurance: Mathematics and Economics, 72, 250264. https://doi.org/10.1016/j.insmatheco.2016.12.002 Google Scholar
Falden, D.K. and Nyegaard, A.K. (2021) Retrospective reserves and bonus with policyholder behavior. Risks, 9(15). https://doi.org/10.3390/risks9010015 Google Scholar
Gerber, H.U. (1997) Life Insurance Mathematics. Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03460-6 CrossRefGoogle Scholar
Gerstner, T., Griebel, M., Holtz, M., Goschnick, R. and Haep, M. (2008) A general asset-liability management model for the efficient simulation of portfolios of life insurance policies. Insurance: Mathematics and Economics, 42(2), 704716. https://doi.org/10.1016/j.insmatheco.2007.07.007 Google Scholar
Gerstner, T., Griebel, M. and Holtz, M. (2009) Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance. Insurance: Mathematics and Economics, 44(3), 434446. https://doi.org/10.1016/j.insmatheco.2008.12.003 Google Scholar
Hochgerner, S. and Gach, F. (2019) Analytical validation formulas for best estimate calculation in traditional life insurance. European Actuarial Journal, 9, 423443. https://doi.org/10.1007/s13385-019-00212-2 CrossRefGoogle Scholar
Laurent, J.-P., Norberg, R. and Planchet, F. (2016) Modelling in Life Insurance – A Management Perspective , EAA Series. Cologne: Springer International Publishing.Google Scholar
O’Brien, C. (2009) Valuation of Life Insurance Liabilities on a Market-Consistent Basis: Experience from the United Kingdom, Actuarial Practice Forum.Google Scholar
Sheldon, T. and Smith, A. (2004) Market consistent valuation of life assurance business. British Actuarial Journal, 10(3), 543605.CrossRefGoogle Scholar
Vedani, J., El Karoui, N., Loisel, S. and Prigent, J.-L. (2017) Market inconsistencies of market-consistent European life insurance economic valuations: Pitfalls and practical solutions. European Actuarial Journal, 7. https://doi.org/10.1007/s13385-016-0141-zCrossRefGoogle Scholar
Verordnung der Finanzmarktaufsichtsbehörde (FMA). Über die Gewinnbeteiligung in der Lebensversicherung.Google Scholar
Wüthrich, M.V. (2016) Market-Consistent Actuarial Valuation, 3rd ed. Springer EAA Series. E-book.CrossRefGoogle Scholar