The Annals of Applied Probability

Mean-variance hedging via stochastic control and BSDEs for general semimartingales

Monique Jeanblanc, Michael Mania, Marina Santacroce, and Martin Schweizer

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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 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.

Article information

Source
Ann. Appl. Probab., Volume 22, Number 6 (2012), 2388-2428.

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1353695957

Digital Object Identifier
doi:10.1214/11-AAP835

Mathematical Reviews number (MathSciNet)
MR3024972

Zentralblatt MATH identifier
1273.60053

Subjects
Primary: 60G48: Generalizations of martingales 60H10: Stochastic ordinary differential equations [See also 34F05] 93E20: Optimal stochastic control 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Keywords
Mean-variance hedging stochastic control backward stochastic differential equations semimartingales mathematical finance variance-optimal martingale measure

Citation

Jeanblanc, Monique; Mania, Michael; Santacroce, Marina; Schweizer, Martin. Mean-variance hedging via stochastic control and BSDEs for general semimartingales. Ann. Appl. Probab. 22 (2012), no. 6, 2388--2428. doi:10.1214/11-AAP835. https://projecteuclid.org/euclid.aoap/1353695957


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