European Actuarial Journal

, Volume 5, Issue 1, pp 11–28 | Cite as

Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees

  • Peter HieberEmail author
  • Ralf Korn
  • Matthias Scherer
Original Research Paper


We analyze the effects of a prevailing low interest rates regime on investment decisions of insurance companies and on the risk/return profile of participating life insurance policies with different contractually guaranteed minimum annual return. Our analysis is based on German legislation and a stylized insurance company with two cohorts of insured persons having different minimal return guarantees. Our findings shed some light on the non-trivial interrelation between profit distribution, minimum guarantees, and resulting profitability for the different cohorts. Moreover, we investigate the complex role of the risk reserve that allows insurance companies to redistribute profits in time and, less obviously, also between the cohorts.


Life insurance policy Minimal return guarantees Surplus distribution 



We want to thank Alexander Kling, Jochen Ruß, Ralf Werner, and the participants of the 2014 research seminar TU München/University Duisburg-Essen for fruitful discussions on the topic.


  1. 1.
    Bacinello A (2003) Fair pricing of a guarantee life insurance participating contract embedding surrender option. J Risk Insur 70(3):461–487MathSciNetCrossRefGoogle Scholar
  2. 2.
    Barbarin J, Devolder P (2005) Risk measure and fair valuation of an investment guarantee in life insurance. Insur Math Econ 37:297–323zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Bauer D, Kiesel R, Kling A, Ruß J (2005) Risk neutral valuation of participating life insurance contracts. Insur Math Econ 39(2):171–183CrossRefGoogle Scholar
  4. 4.
    Bohnert A, Gatzert N (2012) Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective. Insur Math Econ 50(2):64–78zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Bryis E, de Varenne F (1997) On the risk of life insurance liabilities: debunking some common pitfalls. J Risk Insur 64(4):673–694CrossRefGoogle Scholar
  6. 6.
    Døskeland T, Nordahl H (2008) Intergenerational effects of guaranteed pension contracts. In: The Geneva risk and insurance review, vol. 33Google Scholar
  7. 7.
    Goecke O (2013) Pension saving schemes with return smoothing mechanism. Insur Math Econ 53:678–689zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Graf S, Kling A, Ruß J (2011) Risk analysis and valuation of life insurance contracts: combining actuarial and financial approaches. Insur Math Econ 49(10):115–125zbMATHCrossRefGoogle Scholar
  9. 9.
    Grosen J, Jørgensen P (2000) Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options and bonus policies. Insur Math Econ 26(1):37–57zbMATHCrossRefGoogle Scholar
  10. 10.
    Grosen J, Jørgensen P (2002) Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. J Risk Insur 69(1):63–91CrossRefGoogle Scholar
  11. 11.
    Jaquemod R (ed) (2005) Stochastisches Unternehmensmodell für deutsche Lebensversicherungen. VVW, KarlsruheGoogle Scholar
  12. 12.
    Kling A, Ruß J (2004) Differenzierung der Überschüsse konventioneller Lebensversicherungsverträge mit unterschiedlichem Garantiezins: Betrug treuer Kunden oder finanzmathematische Notwendigkeit? Institut für Finanz-und Aktuarwissenschaften UlmGoogle Scholar
  13. 13.
    Patel J, Read C (1996) Handbook of the normal distribution. In: Statistics: a series of textbooks and monographs, 2nd ednGoogle Scholar
  14. 14.
    Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5(2):177–188CrossRefGoogle Scholar

Copyright information

© DAV / DGVFM 2015

Authors and Affiliations

  1. 1.Institut für VersicherungswissenschaftenUniversität UlmUlmGermany
  2. 2.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  3. 3.Fraunhofer ITWMAbteilung FinanzmathematikKaiserslauternGermany
  4. 4.Lehrstuhl für Finanzmathematik (M13)Technische Universität MünchenGarching-HochbrückGermany

Personalised recommendations