Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-013-9213-5· OSTI ID:22309135

Kharroubi, Idris ^[1]; Lim, Thomas ^[2]; Ngoupeyou, Armand ^[3]

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1. Université Paris Dauphine, CEREMADE, CNRS UMR 7534 (France)
2. Université d’Evry and ENSIIE, Laboratoire d’Analyse et Probabilités (France)
3. Université Paris 7, Laboratoire de Probabilités et Modèles Aléatoires (France)

In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.

• OSTI ID: 22309135
• Journal Information: Applied Mathematics and Optimization, Vol. 68, Issue 3; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

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