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A general comparison theorem for backward stochastic differential equations

  • Samuel N. Cohen (a1), Robert J. Elliott (a2) and Charles E. M. Pearce (a1)

Abstract

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.

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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia.
∗∗ Email address: samuel.cohen@adelaide.edu.au
∗∗∗ Postal address: Haskayne School of Business, University of Calgary, Calgary, T2N 1N4, Canada. Email address: relliott@ucalgary.ca
∗∗∗∗ Email address: charles.pearce@adelaide.edu.au

References

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A general comparison theorem for backward stochastic differential equations

  • Samuel N. Cohen (a1), Robert J. Elliott (a2) and Charles E. M. Pearce (a1)

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