Pricing formulae for derivatives in insurance using the Malliavin calculus

Caroline Hillairet, Ying Jiao and Anthony R\'eveillac
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Caroline Hillairet: ENSAE ParisTech
Ying Jiao: SAF
Anthony R\'eveillac: INSA Toulouse, IMT

Papers from arXiv.org

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.

Date: 2017-07
New Economics Papers: this item is included in nep-ias and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1707.05061

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