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

44 Pages Posted: 24 Dec 2011 Last revised: 13 Jun 2012

See all articles by Monique Jeanblanc

Monique Jeanblanc

Université d'Évry - Departement de Mathematiques

Michael Mania

Georgian American University

Marina Santacroce

Polytechnic University of Turin

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: December 15, 2011

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.

Keywords: mean-variance hedging, stochastic control, backward stochastic differential equations, semimartingales, mathematical finance, variance-optimal martingale measure

JEL Classification: G11, C60, C61

Suggested Citation

Jeanblanc, Monique and Mania, Michael and Santacroce, Marina and Schweizer, Martin, Mean-Variance Hedging via Stochastic Control and BSDEs for General Semimartingales (December 15, 2011). Swiss Finance Institute Research Paper No. 11-62, Available at SSRN: https://ssrn.com/abstract=1976235 or http://dx.doi.org/10.2139/ssrn.1976235

Monique Jeanblanc

Université d'Évry - Departement de Mathematiques ( email )

rue du pere Jarlan
F-91025 Evry Cedex
France
33 (0) 1 69 47 02 05/ 02 01 (Phone)
33 (0) 1 69 47 02 18 (Fax)

Michael Mania

Georgian American University ( email )

17a, ChavchavadzeAve
Tbilisi
Georgia

Marina Santacroce

Polytechnic University of Turin ( email )

Corso Duca degli Abruzzi, 24
Torino, Torino 10129
Italy

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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