The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims

Stéphane Goutte and Armand Ngoupeyou ()
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Armand Ngoupeyou: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we consider the problem of mean-variance hedging of a defaultable claim. We assume the underlying assets are jump processes driven by Brownian motion and default processes. Using the dynamic programming principle, we link the existence of the solution of the mean-variance hedging problem to the existence of solution of a system of coupled backward stochastic differential equations (BSDEs). First we prove the existence of a solution to this system of coupled BSDEs. Then we give the corresponding solution to the mean variance hedging problem. Finally, we give some existence conditions and characterize the well known variance optimal martingale measure (VOMM) using the solution to the first quadratic BSDE with jumps that we derived from the previous stochastic control problem. We conclude with an explicit example of our credit risk model giving a numerical application in a two defaults case

Date: 2015
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Citations: View citations in EconPapers (2)

Published in Stochastic Processes and their Applications, 2015, 125 (4), pp.1323-1351. ⟨10.1016/j.spa.2014.10.017⟩

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Journal Article: The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02879222

DOI: 10.1016/j.spa.2014.10.017

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