Pricing formulae for derivatives in insurance using the Malliavin calculus *Report as inadecuate




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1 ENSAE ParisTech - École Nationale de la Statistique et de l-Administration Économique 2 SAF - Laboratoire de Sciences Actuarielle et Financière 3 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse 4 IMT - Institut de Mathématiques de Toulouse UMR5219

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.





Author: Caroline Hillairet - Ying Jiao - Anthony Réveillac -

Source: https://hal.archives-ouvertes.fr/



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