The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 6 (2012), 2388-2428.
Mean-variance hedging via stochastic control and BSDEs for general semimartingales
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.
Ann. Appl. Probab., Volume 22, Number 6 (2012), 2388-2428.
First available in Project Euclid: 23 November 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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