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

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  • Chaudru de Raynal, P.E.
  • Garcia Trillos, C.A.

Abstract

We propose a new algorithm to approximate weakly the solution of a McKean–Vlasov SDE. Based on the cubature method of Lyons and Victoir (2004), the algorithm is deterministic differing from the usual methods based on interacting particles. It can be parametrized in order to obtain a given order of convergence.

Suggested Citation

  • Chaudru de Raynal, P.E. & Garcia Trillos, C.A., 2015. "A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2206-2255.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:6:p:2206-2255
    DOI: 10.1016/j.spa.2014.11.018
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    References listed on IDEAS

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    1. Crisan Dan & Lyons Terry, 2002. "Minimal Entropy Approximations and Optimal Algorithms," Monte Carlo Methods and Applications, De Gruyter, vol. 8(4), pages 343-356, December.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    3. Imkeller, Peter & Dos Reis, Gonçalo, 2010. "Path regularity and explicit convergence rate for BSDE with truncated quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 348-379, March.
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