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December 2012 Mean-variance hedging via stochastic control and BSDEs for general semimartingales
Monique Jeanblanc, Michael Mania, Marina Santacroce, Martin Schweizer
Ann. Appl. Probab. 22(6): 2388-2428 (December 2012). DOI: 10.1214/11-AAP835


We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing literature, we provide alternative equivalent versions of the BSDEs and present a number of simple examples.


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Monique Jeanblanc. Michael Mania. Marina Santacroce. Martin Schweizer. "Mean-variance hedging via stochastic control and BSDEs for general semimartingales." Ann. Appl. Probab. 22 (6) 2388 - 2428, December 2012.


Published: December 2012
First available in Project Euclid: 23 November 2012

zbMATH: 1273.60053
MathSciNet: MR3024972
Digital Object Identifier: 10.1214/11-AAP835

Primary: 60G48 , 60H10 , 91G80 , 93E20

Keywords: Backward stochastic differential equations , mathematical finance , Mean-variance hedging , Semimartingales , Stochastic control , variance-optimal martingale measure

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.22 • No. 6 • December 2012
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