Backward stochastic differential equations and stochastic controls

Type of Publication: Contribution to a conference collection
Author: Kohlmann, Michael; Zhou, Xun Yu
Year of publication: 1999
Conference: 1999 Conference on Decision and Control, Phoenix, AZ, USA
Published in: Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304). - IEEE, 1999. - pp. 2384-2389. - ISBN 0-7803-5250-5
DOI (citable link): https://dx.doi.org/10.1109/CDC.1999.831281
Summary:
The paper attempts to explore the relationship between backward stochastic differential equations (BSDEs) and stochastic controls by interpreting a BSDE as some stochastic optimal control problem. The latter is solved in a closed form by the stochastic linear-quadratic (LQ) theory. The general result is then applied to the Black-Scholes model, where an optimal mean-variance hedging portfolio is obtained explicitly in terms of the option price. Finally, a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account.
Subject (DDC): 510 Mathematics

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KOHLMANN, Michael, Xun Yu ZHOU, 1999. Backward stochastic differential equations and stochastic controls. 1999 Conference on Decision and Control. Phoenix, AZ, USA. In: Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304). IEEE, pp. 2384-2389. ISBN 0-7803-5250-5. Available under: doi: 10.1109/CDC.1999.831281

@inproceedings{Kohlmann1999Backw-25846, title={Backward stochastic differential equations and stochastic controls}, year={1999}, doi={10.1109/CDC.1999.831281}, isbn={0-7803-5250-5}, publisher={IEEE}, booktitle={Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)}, pages={2384--2389}, author={Kohlmann, Michael and Zhou, Xun Yu} }

Kohlmann, Michael Backward stochastic differential equations and stochastic controls The paper attempts to explore the relationship between backward stochastic differential equations (BSDEs) and stochastic controls by interpreting a BSDE as some stochastic optimal control problem. The latter is solved in a closed form by the stochastic linear-quadratic (LQ) theory. The general result is then applied to the Black-Scholes model, where an optimal mean-variance hedging portfolio is obtained explicitly in terms of the option price. Finally, a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account. 2014-01-15T08:27:30Z Zhou, Xun Yu Proceedings of the 38th IEEE Conference on Decision and Control : December 7-10, 1999, Crowne Plaza Hotel & Resort, Phoenix, Arizona, USA / IEEE Control Systems Society. - Piscataway, N.J. : IEEE Service Center, 1999. - S. 2384 - 2389. - ISBN 0-7803-5250-5 Zhou, Xun Yu eng terms-of-use 2014-01-15T08:27:30Z Kohlmann, Michael 1999

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