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

Idris Kharroubi 1 Thomas Lim 2 Armand Ngoupeyou 2
1 CEREMADE
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
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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Applied Mathematics and Optimization, 2013, 68, pp.413 - 444. <10.1007/s00245-013-9213-5>
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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, 2013, 68, pp.413 - 444. <10.1007/s00245-013-9213-5>. <hal-01103691>

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