Built on

N. El Karoui, S. Peng, and M. C. Quenez, Backward stochastic differential equations in finance , Math. Finance, 7 (1997), pp. 1–71
1997
Earlier work this paper cites.
S. Peng and Z. Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control , SIAM J. Control Optim., 37 (1999), pp. 825–843
1999
Earlier work this paper cites.
F. Delarue, On the existence and uniqueness of solutions to FBSDEs in a nondegenerate case , Stochastic Process. Appl., 99 (2002), pp. 209–286
2002
Earlier work this paper cites.
J. Zhang, A numerical scheme for BSDEs , Ann. Appl. Probab. 14 (2004), pp. 459–488
2004
Earlier work this paper cites.
D. Nualart, The Malliavin Calculus and Related Topics , 2nd ed., Springer-Verlag, Berlin, 2006
2006
Earlier work this paper cites.
C. Bender and J. Zhang, Time discretization and Markovian iteration for coupled FBSDEs , Ann. Appl. Probab., 18 (2008), pp. 143–177
2008
Earlier work this paper cites.

Similar

J. Zhang, Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory , vol. 86., Springer, New York, 2017
Original
2011
Cited alongside, same era.
A. Bensoussan, S. Yam, and Z. Zhang, Well-posedness of mean-field type forward-backward stochastic differential equations , Stochastic Process. Appl., 125 (2015), pp. 3327–3354
2015
Cited alongside, same era.
R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics , Ann. Probab., 43 (2015), pp. 2647–2700
2015
Cited alongside, same era.
A. Lionnet, G. dos Reis, and L. Szpruch, Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs , Ann. Appl. Probab., 25 (2015), pp. 2563–2625
2015
Cited alongside, same era.
E. Bandini, A. Cosso, M. Fuhrman, and H. Pham, Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem , arXiv preprint, arXiv:1609.02697, 2016

Then

E. Gobet and M. Grangereau, Extended McKean-Vlasov optimal stochastic control applied to smart grid management , at hal-02181227, 2019
2019
Later among the works it cites.
M. Laurière and L. Tangpi, Backward propagation of chaos , arXiv preprint, arXiv:1911.06835, 2019
Original
2019
Later among the works it cites.
J. F. Chassagneux, D. Crisan, and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria , Mem. Amer. Math. Soc., (2020), Available at arXiv:1411.3009
Original
2020
Closest in time.
C. Reisinger, W. Stockinger, and Y. Zhang, A posteriori error estimates for fully coupled McKean-Vlasov forward-backward SDEs , arXiv preprint, arXiv:2007.07731, 2020
Original
2020
Closest in time.
C. Reisinger, W. Stockinger, and Y. Zhang, Optimal regularity of extended mean field controls and their piecewise constant approximation , arXiv preprint, arXiv:2009.08175v2, 2020

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2020

Path regularity of coupled McKean-Vlasov FBSDEs

Reisinger, Christoph, Stockinger, Wolfgang, Zhang, Yufei

Understand

This paper establishes H\"{o}lder time regularity of solutions to coupled McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs).

This is not only of fundamental mathematical interest, but also essential for their numerical approximations.
We show that a solution triple to a MV-FBSDE with Lipschitz coefficients is 1/2-H\"{o}lder continuous in time in the $L^p$-norm provided that it admits a Lipschitz decoupling field.
Special examples include decoupled MV-FBSDEs, coupled MV-FBSDEs with a small time horizon and coupled stochastic Pontryagin systems arsing from mean field control problems.

Built on

N. El Karoui, S. Peng, and M. C. Quenez, Backward stochastic differential equations in finance , Math. Finance, 7 (1997), pp. 1–71
1997
Earlier work this paper cites.
S. Peng and Z. Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control , SIAM J. Control Optim., 37 (1999), pp. 825–843
1999
Earlier work this paper cites.
F. Delarue, On the existence and uniqueness of solutions to FBSDEs in a nondegenerate case , Stochastic Process. Appl., 99 (2002), pp. 209–286
2002
Earlier work this paper cites.
J. Zhang, A numerical scheme for BSDEs , Ann. Appl. Probab. 14 (2004), pp. 459–488
2004
Earlier work this paper cites.
D. Nualart, The Malliavin Calculus and Related Topics , 2nd ed., Springer-Verlag, Berlin, 2006
2006
Earlier work this paper cites.
C. Bender and J. Zhang, Time discretization and Markovian iteration for coupled FBSDEs , Ann. Appl. Probab., 18 (2008), pp. 143–177
2008
Earlier work this paper cites.

Similar

J. Zhang, Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory , vol. 86., Springer, New York, 2017
Original
2011
Cited alongside, same era.
A. Bensoussan, S. Yam, and Z. Zhang, Well-posedness of mean-field type forward-backward stochastic differential equations , Stochastic Process. Appl., 125 (2015), pp. 3327–3354
2015
Cited alongside, same era.
R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics , Ann. Probab., 43 (2015), pp. 2647–2700
2015
Cited alongside, same era.
A. Lionnet, G. dos Reis, and L. Szpruch, Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs , Ann. Appl. Probab., 25 (2015), pp. 2563–2625
2015
Cited alongside, same era.
E. Bandini, A. Cosso, M. Fuhrman, and H. Pham, Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem , arXiv preprint, arXiv:1609.02697, 2016

Then

E. Gobet and M. Grangereau, Extended McKean-Vlasov optimal stochastic control applied to smart grid management , at hal-02181227, 2019
2019
Later among the works it cites.
M. Laurière and L. Tangpi, Backward propagation of chaos , arXiv preprint, arXiv:1911.06835, 2019
Original
2019
Later among the works it cites.
J. F. Chassagneux, D. Crisan, and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria , Mem. Amer. Math. Soc., (2020), Available at arXiv:1411.3009
Original
2020
Closest in time.
C. Reisinger, W. Stockinger, and Y. Zhang, A posteriori error estimates for fully coupled McKean-Vlasov forward-backward SDEs , arXiv preprint, arXiv:2007.07731, 2020
Original
2020
Closest in time.
C. Reisinger, W. Stockinger, and Y. Zhang, Optimal regularity of extended mean field controls and their piecewise constant approximation , arXiv preprint, arXiv:2009.08175v2, 2020

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2016

Cited alongside, same era.

R. Carmona and F. Delarue, Probabilistic theory of mean field games with applications I: Mean-field FBSDEs, control, and games , Springer International Publishing, Switzerland, 2018

2018

Cited alongside, same era.

Original

2020

Closest in time.