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Pricing formulae for derivatives in insurance using the Malliavin calculus

Author

Listed:
  • Caroline Hillairet

    (ENSAE; Université Paris Saclay)

  • Ying Jiao

    (Université Claude Bernard - Lyon 1; Institut de Science Financière et d’Assurances)

Abstract

In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is related to the loss process which is a cumulated sum indexed by a doubly stochastic Poisson process of claims allowed to be dependent on the intensity and the jump times of the counting process. For example, in the context of Stop-Loss contracts the building block is given by the distribution function of the terminal cumulated loss, taken at the Value at Risk when computing the Expected Shortfall risk measure.

Suggested Citation

  • Caroline Hillairet & Ying Jiao, 2017. "Pricing formulae for derivatives in insurance using the Malliavin calculus," Working Papers 2017-75, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-75
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    References listed on IDEAS

    as
    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
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    8. repec:cup:astinb:v:12:y:1981:i:01:p:22-26_00 is not listed on IDEAS
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