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Mean-Variance Hedging via Stochastic Control and BSDEs for General Semimartingales

Monique Jeanblanc 

Université d'Évry - Departement de Mathematiques

Michael Mania 

Georgian American University

Marina Santacroce 

Polytechnic University of Turin

Martin Schweizer 

ETH Zürich - Department of Mathematics
December 15, 2011

Swiss Finance Institute Research Paper No. 11-62 
Abstract:      
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 characterise 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.