European Actuarial Journal

, Volume 9, Issue 2, pp 423–443 | Cite as

Analytical validation formulas for best estimate calculation in traditional life insurance

  • Simon HochgernerEmail author
  • Florian Gach
Original Research Paper


Within the context of traditional life insurance, a model-independent relationship about how the market value of assets is attributed to the best estimate, the value of in-force business and tax is established. This relationship holds true for any portfolio under run-off assumptions and can be used for the validation of models set up for Solvency II best estimate calculation. Furthermore, we derive a lower bound for the value of future discretionary benefits. This lower bound formula is applied to publicly available insurance data to show how it can be used for practical validation purposes.


Solvency II Best estimate Asset liability management Market consistent valuation 



We thank the anonymous reviewers for their detailed and helpful input.


  1. 1.
    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
  2. 2.
    Sheldon T, Smith A (2004) Market consistent valuation of life assurance business. Br Actuar J 10(3):543–605CrossRefGoogle Scholar
  3. 3.
    O’Brien C (2009) Valuation of life insurance liabilities on a market-consistent basis: experience from the United Kingdom. Actuarial Practice Forum by the Society of ActuariesGoogle Scholar
  4. 4.
    Vedani J, El Karoui N, Loisel S, Prigent J-L (2017) Market inconsistencies of market-consistent European life insurance economic valuations: pitfalls and practical solutions. Eur Actuar J 7:1–28MathSciNetCrossRefGoogle Scholar
  5. 5.
    Delong L (2011) Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities. Bank i Kredyt Narodowy Bank Polski 42(1):49–78MathSciNetGoogle Scholar
  6. 6.
    Laurent J-P, Norberg R, Planchet F (2016) Modelling in life insurance—a management perspective, EAA series. Springer International Publishing, New YorkCrossRefGoogle Scholar
  7. 7.
  8. 8.
    EIOPA-BoS-16/302, 2016 EIOPA insurance stress test reportGoogle Scholar
  9. 9.
    Gerber H (1997) Life insurance mathematics. Springer, BerlinCrossRefGoogle Scholar
  10. 10.
    Bundesgesetz über den Betrieb und die Beaufsichtigung der Vertragsversicherung (Versicherungsaufsichtsgesetz 2016—VAG 2016)Google Scholar
  11. 11.
    Filipovic D (2009) Term-structure models. Springer Finance Textbooks, BerlinCrossRefGoogle Scholar
  12. 12.
    Teichmann J, Wüthrich M (2012) Consistent long-term yield prediction. arXiv:1203.2017
  13. 13.
    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
  14. 14.
    CFO Forum (2016) Market consistent embedded value principles. Accessed 1 Feb 2019
  15. 15.
    Laimer K (2015) Zinsszenarien und Best Estimate in der Lebensversicherung, Diploma Thesis, TU ViennaGoogle Scholar
  16. 16.
    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 CouncilGoogle Scholar
  17. 17.
    Allianz Lebensversicherungs AG (2017) Bericht über Solvabilität und Finanzlage. Accessed 1 Feb 2019
  18. 18.
    Allianz Lebensversicherungs AG (2017) Geschäftsbericht. Accessed 1 Feb 2019
  19. 19.
    BaFin Auslegungsentscheidungen, Überschussfonds nach Art. 91 der Solvency II Richtlinie. Accessed 1 Feb 2019
  20. 20.
    Verordnung der Finanzmarktaufsichtsbehörde (FMA) über die Gewinnbeteiligung in der LebensversicherungGoogle Scholar
  21. 21.
    Mindestzuführungsverordnung (MindZV). Accessed 1 Feb 2019
  22. 22.
    Kemp M (2009) Market consistency: model calibration in imperfect markets. Wiley, New YorkGoogle Scholar
  23. 23.

Copyright information

© EAJ Association 2019

Authors and Affiliations

  1. 1.Austrian Financial Market AuthorityViennaAustria

Personalised recommendations