A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations

Raynal, Paul Éric Chaudru de; Trillos, Camilo A. Garcia

doi:10.1016/j.spa.2014.11.018

Cited by 33 publications

(20 citation statements)

References 37 publications

(70 reference statements)

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“…In [25] it is shown that this algorithm with this choice of approximation law leads to a first order approximation scheme of Y (more precisely, the infinity norm of the approximation error decreases linearly with the number of discretization steps). It is also possible to obtain higher orders of approximation by correcting some terms in the algorithm and to relax the regularity of φ in (12) to Lipschitz, provided the vector fields are uniformly elliptic.…”

Section: Resultsmentioning

confidence: 99%

“…Lions in a series of papers [50][51][52][53] (see the work of Carmona and Delarue [18] for the probabilistic analysis) and also in physics, neuroscience, dynamic population models etc... Here, this system can be also viewed as the probabilistic representation of a control problem of a marked player in a mean field environment [25].…”

Section: The Systemmentioning

confidence: 99%

“…We fix T, h > 0, p ∈ N and we assume that the short time estimates (15) and (20) hold (with this p and h). Moreover, we assume (24), (25), (26) and (27) and that (17) holds for the semigroup P t k . Then, we have the following results.…”

Section: Estimates Of the Error In The Total Variation Distancementioning

confidence: 99%

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Recent advances in various fields of numerical probability

et al. 2015

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Abstract. The goal of this paper is to present a series of recent contributions on some various problems of numerical probability. Beginning with the Richardson-Romberg Multilevel Monte-Carlo method which, among other fields of applications, is a very efficient method for the approximation of diffusion processes, we focus on some adaptive multilevel splitting algorithms for rare event simulation. Then, the third part is devoted to the simulation of McKean-Vlasov forward and decoupled forwardbackward stochastic differential equations by some cubature algorithms. Finally, we tackle the problem of the weak error estimation in total variation norm for a general Markov semi-group.

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Section: Resultsmentioning

confidence: 99%

Section: The Systemmentioning

confidence: 99%

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Recent advances in various fields of numerical probability

et al. 2015

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“…More recently, two other works [2,13] give some partial results related to the smoothness of the solutions of McKean-Vlasov SDEs. In [2], the Malliavin differentiability of McKean-Vlasov SDEs is studied using a stochastic perturbation approach of Bismut type.…”

Section: Comparison With Other Workmentioning

confidence: 99%

“…In [2], the Malliavin differentiability of McKean-Vlasov SDEs is studied using a stochastic perturbation approach of Bismut type. In [13], the strong well-posedness of a McKean-Vlasov SDEs is proven when the diffusion matrix is Lipschitz with respect to both the space and measure arguments and uniformly elliptic and the drift is bounded in space and Hölder continuous in the measure direction. Both works restrict themselves to the particular case when the coefficient dependence on the law of the solution is of scalar type.…”

Section: Comparison With Other Workmentioning

confidence: 99%

Smoothing properties of McKean–Vlasov SDEs

Crisan

McMurray

2017

Probab. Theory Relat. Fields

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In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives of the density of the solutions of McKean-Vlasov SDEs.

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A higher order weak approximation of McKean–Vlasov type SDEs

Naito

Yamada

2021

Bit Numer Math

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A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations

Cited by 33 publications

References 37 publications

Recent advances in various fields of numerical probability

Recent advances in various fields of numerical probability

Smoothing properties of McKean–Vlasov SDEs

A higher order weak approximation of McKean–Vlasov type SDEs

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