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

By Idris Kharroubi, Thomas Lim and Armand Ngoupeyou

Abstract

International audienceIn 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

Topics: Backward SDE, random horizon, decomposition in the reference filtration AMS subject classifications: 91B30, pro-gressive enlargement of filtration, jump processes, Mean-variance hedging, 93E20, 60H10, 60G57, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2013
DOI identifier: 10.1007/s00245-013-9213-5
OAI identifier: oai:HAL:hal-01103691v1
Provided by: Hal-Diderot

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