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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01103691
Contributor : Idris Kharroubi <>
Submitted on : Thursday, January 15, 2015 - 11:24:34 AM
Last modification on : Saturday, April 3, 2021 - 3:17:17 AM
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Idris Kharroubi, Thomas Lim, Armand Ngoupeyou. Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump. Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68, pp.413 - 444. ⟨10.1007/s00245-013-9213-5⟩. ⟨hal-01103691⟩

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