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Pricing formulae for derivatives in insurance using Malliavin calculus

The authors acknowledge anonymous referees and the Associate Editor for comments and suggestions that have allowed us to improve the paper. The authors acknowledge Projet PEPS égalité (part of the European project INTEGER-WP4) "Approximation de Stein:approche par calcul de Malliavin et applications à la gestion des risques financiers" for financial support.
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  • 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 Malliavin calculus. Similar to the celebrated Black-Scholes formula, we aim to express 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.


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