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A general comparison theorem for backward stochastic differential equations

Part of: Stochastic systems and control Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Samuel N. Cohen ,
Robert J. Elliott  and
Charles E. M. Pearce
Samuel N. Cohen*
Affiliation:
University of Adelaide
Robert J. Elliott*
Affiliation:
University of Adelaide and University of Calgary
Charles E. M. Pearce*
Affiliation:
University of Adelaide
*
∗ Postal address: School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia.
∗∗∗ Postal address: Haskayne School of Business, University of Calgary, Calgary, T2N 1N4, Canada. Email address: relliott@ucalgary.ca
∗ Postal address: School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia.
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Abstract

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A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectations are also explored.

Keywords

BSDEcomparison theoremnonlinear expectationdynamic risk measure

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 3 , September 2010 , pp. 878 - 898
Copyright
Copyright © Applied Probability Trust 2010 

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