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5 juin 2018
- handle: 10670/1.3v3f67
- hal: hal-01561987
- ARXIV: 1707.05061
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info:eu-repo/semantics/altIdentifier/arxiv/1707.05061
info:eu-repo/semantics/OpenAccess
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-fin]/Computational Finance [q-fin.CP]Sujets proches
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Caroline Hillairet et al., « Pricing formulae for derivatives in insurance using the Malliavin calculus * », HAL-SHS : économie et finance, ID : 10670/1.3v3f67
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Résumé
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.