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

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. Applied Mathematics and Optimization Springer Journals

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

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Springer US
Copyright © 2013 by Springer Science+Business Media New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
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  • An extension of mean-variance hedging to the discontinuous case
    Arai, T.

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