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

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.
Authors:
 [1] ;  [2] ;  [3]
  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)
Publication Date:
OSTI Identifier:
22309135
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal 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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; RANDOMNESS; STOCHASTIC PROCESSES; UNCERTAINTY PRINCIPLE