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Backward Stochastic Differential Equations

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Stochastic Calculus and Applications

Part of the book series: Probability and Its Applications ((PA))

Abstract

In this chapter, we consider a different type of stochastic differential equation. In the setting of Chapter 17, we specified a solution process X through its dynamics and its initial value, as in (17.6). In this chapter, we specify a solution process Y through its dynamics and its terminal value, at a fixed, deterministic time \(T \in ]0,\infty [\). The difficulty with this is that the terminal value is allowed to be a random variable, but we look for a solution which is adapted to a given filtration.

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Notes

  1. 1.

    This is because any closed, convex and bounded set in L 2(ν) is weakly compact, and so any bounded sequence has a weak limit in the space (Theorem 1.7.19). Using Theorem A.10.5, this weak limit can be chosen to be measurable in its other arguments.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, UK

    Samuel N. Cohen

  2. School of Mathematics, University of Adelaide, Adelaide, Australia

    Robert J. Elliott

  3. Haskayne School of Business, University of Calgary, Calgary, Canada

    Robert J. Elliott

Authors
  1. Samuel N. Cohen
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  2. Robert J. Elliott
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Cohen, S.N., Elliott, R.J. (2015). Backward Stochastic Differential Equations. In: Stochastic Calculus and Applications. Probability and Its Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-2867-5_19

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