Backward stochastic differential equations with Young drift

Joscha Diehl; Jianfeng Zhang

doi:10.1186/s41546-017-0016-5

Article Contents

2017, Volume 2: 5. Doi: 10.1186/s41546-017-0016-5

This volume Previous Article A brief history of quantitative finance Next Article Convergence to a self-normalized G-Brownian motion

Backward stochastic differential equations with Young drift

Joscha Diehl^1, , and
Jianfeng Zhang^2, ,

1 Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany;
2 Department of Mathematics, University of Southern California, Los Angeles, California, USA

Joscha Diehl, diehl@mis.mpg.de ; Jianfeng Zhang, jianfenz@usc.edu

Received: October 27, 2016

Revised: March 25, 2017

Published: September 2020

This research was partially supported by the DAAD P.R.I.M.E. program and NSF grant DMS 1413717.

Abstract Related Papers Cited by

Abstract

We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q ∈[1, 2). In contrast to previous work, we apply a direct fixpoint argument and do not rely on any type of flow decomposition. The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman-Kac type representation.

Keywords:

Citation:

Related Papers

Cited by

References

[1]	Bismut, J-M:Conjugate Convex Functions in Optimal Stochastic Control. J.Math. Anal. Apl 44, 384-404(1973)
[2]	Caruana, M, Friz, PK, Oberhauser, H:A (rough) pathwise approach to a class of non-linear stochastic partial differential equations. Ann. Inst. Henri Poincare (C) Non Linear Anal 28(1), 27-46 (2011)
[3]	Dan, C, et al:Robust filtering:correlated noise and multidimensional observation. Ann. Appl. Probab 23.5, 2139-2160 (2013)
[4]	Diehl, J, Friz, P:Backward stochastic differential equations with rough drivers. Ann. Probab. 40.4, 1715-1758 (2012)
[5]	Diehl, J, Oberhauser, H, Riedel, S:A Levy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations. Stochastic Process. Appl 125.1, 161-181 (2015)
[6]	Diehl, J, Friz, PK, Stannat, W:Stochastic partial differential equations:a rough path view (2014). arXiv preprint arXiv:1412.6557
[7]	El Karoui, N, Peng, S, Quenez, M-C:Backward stochastic differential equations in finance. Math. Finance 7.1, 1-71 (1997)
[8]	Friz, PK, Victoir, NB:Multidimensional stochastic processes as rough paths:theory and applications, vol. 120. Cambridge University Press (2010)
[9]	Friz, P, Hairer, M:A course on rough paths. Springer Heidelberg (2014)
[10]	Guerra, J, Nualart, D:Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion. Stochastic Anal. Appl 26.5, 1053-1075 (2008)
[11]	Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. Syst. Control Lett 14.1, 55-61 (1990)
[12]	Pardoux, E, Peng, S:Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic Partial differential equations and their applications, pp. 200-217. Springer Berlin Heidelberg (1992)
[13]	Stroock, DW, Karmakar, S:Lectures on topics in stochastic differential equations. Tata Institute of Fundamental Research, Bombay (1982)
[14]	Young, LC:An inequality of the Hölder type, connected with Stieltjes integration. Acta Math 67(1), 251-282 (1936)