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Optimal Control of Linear Backward Stochastic Differential Equations with a Quadratic Cost Criterion

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Stochastic Theory and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 280))

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Abstract

Backward Stochastic Differential Equations (BSDEs) are Ito SDEs with a random terminal condition. While it is the case that uncontrolled BSDEs have been the topic of extensive research for a number of years, little has been done on optimal control of BSDEs. In this paper, we consider the problem of linear-quadratic control of a BSDE. A complete solution to this problem is obtained, in terms of a pair of Riccati type equations and an uncontrolled BSDE, using an approach that is based on the completion of squares technique.

The research of this author was supported by the RGC Earmarked Grants CUHK 4435/99E.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY, 10027, USA

    Andrew E. B. Lim

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Xun Yu Zhou

Authors
  1. Andrew E. B. Lim
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  2. Xun Yu Zhou
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Editor information

Editors and Affiliations

  1. Dep. of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS, 66045, USA

    Bozenna Pasik-Duncan

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© 2002 Springer-Verlag Berlin Heidelberg

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Lim, A.E.B., Zhou, X.Y. (2002). Optimal Control of Linear Backward Stochastic Differential Equations with a Quadratic Cost Criterion. In: Pasik-Duncan, B. (eds) Stochastic Theory and Control. Lecture Notes in Control and Information Sciences, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48022-6_21

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  • DOI: https://doi.org/10.1007/3-540-48022-6_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43777-2

  • Online ISBN: 978-3-540-48022-8

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