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European Actuarial Journal

, Volume 5, Issue 1, pp 55–77 | Cite as

Best-estimate claims reserves in incomplete markets

  • Sebastian Happ
  • Michael Merz
  • Mario V. Wüthrich
Original Research Paper

Abstract

We give a rigorous definition of best-estimates reserves for insurance liabilities in a general multiperiod financial market setting. In this general multiperiod financial market setting we describe payoff spaces and optimal dynamic hedging strategies. Based on this optimal dynamic hedging strategies we define best-estimate reserves for insurance liabilities. One crucial observation is that we need the notion of optimal hedging and state-price deflators because there does not necessarily exist an equivalent probability measure under which best-estimate reserves can be calculated.

Keywords

Best-estimate reserves Dynamic hedging sequential local risk minimization State-price deflator Incomplete market Technical provisions Risk margin 

References

  1. 1.
    Bühlmann H, Gisler A (2005) A course in credibility theory and its applications. Springer, BerlinMATHGoogle Scholar
  2. 2.
    \(\breve{{\rm C}}\)erný A, Kallsen J (2009) Hedging by sequential regressions revisited. Math Fin 19(4):591–617Google Scholar
  3. 3.
    Eisele K-T, Artzner P (2011) Multiperiod insurance supervision: top-down models. Eur Actuarial J 1(1):107–130MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    European Commission (2009) Framework Solvency II Directive (Directive 2009/138/EC)Google Scholar
  5. 5.
    Föllmer H, Schweizer M (1988) Hedging by sequential regression: an introduction to the mathematics of option trading. Astin Bull 18(2):147–160CrossRefGoogle Scholar
  6. 6.
    Malamud S, Trubowitz E (2007) The structure of optimal consumption streams in general incomplete markets. Math Fin Econ 1(2):129–161MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Malamud S, Trubowitz E, Wüthrich MV (2008) Market consistent pricing of insurance products. Astin Bull 38(2):483–526MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Malamud S, Trubowitz E, Wüthrich MV (2013) Indifference pricing for CRRA utilities. Math Fin Econ 7(3):247–280MATHCrossRefGoogle Scholar
  9. 9.
    Natolski J, Werner R (2014) Mathematical analysis of different approaches for replicating portfolios. Eur Actuarial J 4(2):411–435Google Scholar
  10. 10.
    Wüthrich MV (2013) Non-life insurance: mathematics and statistics. SSRN preprint 2319328, version of 2 December 2013Google Scholar
  11. 11.
    Wüthrich MV, Merz M (2013) Financial modeling, actuarial valuation and solvency in insurance. Springer, New YorkMATHCrossRefGoogle Scholar

Copyright information

© DAV / DGVFM 2014

Authors and Affiliations

  • Sebastian Happ
    • 1
  • Michael Merz
    • 1
  • Mario V. Wüthrich
    • 2
    • 3
  1. 1.Faculty of Business AdministrationUniversity of HamburgHamburgGermany
  2. 2.Department of MathematicsETH Zurich, RiskLabZurichSwitzerland
  3. 3.Swiss Finance InstituteZurichSwitzerland

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