Anticipated backward stochastic differential equations

2007/05/31 by Shige Peng, Zhe Yang · 1 citation
Mathematics · #math.PR #msc:60H10 #msc:60H20 #msc:93E03

paper · pdf · doi:10.1214/08-aop423

published as Annals of Probability 2009, Vol. 37, No. 3, 877-902 · Published in at http://dx.doi.org/10.1214/08-AOP423 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2009/06/26 · arxiv updated 2014/06/30

Abstract

In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.

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