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The value of a liability cash flow in discrete time subject to capital requirements

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  • Hampus Engsner
  • Kristoffer Lindensjo
  • Filip Lindskog

Abstract

The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the approach presented is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner's perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.

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  • Hampus Engsner & Kristoffer Lindensjo & Filip Lindskog, 2018. "The value of a liability cash flow in discrete time subject to capital requirements," Papers 1808.03328, arXiv.org.
    • Handle: RePEc:arx:papers:1808.03328
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    References listed on IDEAS

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    1. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Other publications TiSEM 0841e78f-a73b-42c1-b7d4-0, Tilburg University, School of Economics and Management.
    2. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    3. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    4. 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.
    5. Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    6. John Hancock & Paul Huber & Pablo Koch, 2001. "Value Creation in the Insurance Industry," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 4(2), pages 1-9, September.
    7. Detlefsen, Kai & Scandolo, Giacomo, 2005. "Conditional and dynamic convex risk measures," SFB 649 Discussion Papers 2005-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    9. Malamud, Semyon & Trubowitz, Eugene & Wüthrich, Mario V., 2008. "Market Consistent Pricing of Insurance Products," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 483-526, November.
    10. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    11. Jan Natolski & Ralf Werner, 2017. "Mathematical Analysis of Replication by Cash Flow Matching," Risks, MDPI, vol. 5(1), pages 1-15, February.
    12. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
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