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Title: Pricing cumulative loss derivatives under additive models via Malliavin calculus
Author: Khalfallah, Mohammed El-arbi
Hadji, Mohammed Lakhdar
Vives i Santa Eulàlia, Josep, 1963-
Keywords: Actius financers derivats
Teoria de jocs
Càlcul de Malliavin
Anàlisi estocàstica
Derivative securities
Game theory
Malliavin calculus
Analyse stochastique
Issue Date: 11-Oct-2020
Publisher: Sociedade Paranaense de Matemática
Abstract: We show that the integration by parts formula based on Malliavin-Skorohod calculus techniques for additive processes helps us to compute quantities like $\mathbb{E}\left(L_{T} h\left(L_{T}\right)\right)$, or more generally $\mathbb{E}\left(H\left(L_{T}\right)\right)$, for different suitable functions $h$ or $H$ and different models for the cumulative loss process $L .$ These quantities are important in Insurance and Finance. For example they appear in computing expected shortfall risk measures or prices of stop-loss contracts. The formulas given in the present paper generalize the formulas given in a recent paper by Hillairet, Jiao and Réveillac (HJR). In the HJR paper, despite the use of advanced models, including the Cox process, the treatment of the formulas is based only on Malliavin calculus techniques for the standard Poisson process, a particular case of additive process. In the present paper, Malliavin calculus techniques for additive processes are used, more general results are obtained and proofs appears to be shorter.
Note: Reproducció del document publicat a:
It is part of: Boletim da Sociedade Paranaense de Matemática, 2020, vol. 40
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ISSN: 0037-8712
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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