Backward stochastic differential equations and stochastic controls

Kohlmann, Michael; Zhou, Xun Yu

Backward stochastic differential equations and stochastic controls

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Date

1999

Authors

Kohlmann, Michael

Zhou, Xun Yu

Publication type

Contribution to a conference collection

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

Abstract

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

Conference

1999 Conference on Decision and Control, Phoenix, AZ, USA

Cite This

ISO 690

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

BibTex

@inproceedings{Kohlmann1999Backw-25846,
  year={1999},
  doi={10.1109/CDC.1999.831281},
  title={Backward stochastic differential equations and stochastic controls},
  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}
}

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