A cubature based algorithm to solve decoupled McKean-Vlasov Forward Backward Stochastic Differential Equations
Preprint
Abstract
We propose a new algorithm to approach 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 the usual methods based on interacting particles. It can be parametrized in order to obtain a given order of convergence. Then, we construct implementable algorithms to solve decoupled Forward Backward Stochastic Differential equations (FBSDE) of McKean-Vlasov type, which appear in some stochastic control problems in a mean field environment. We give two algorithms and show that they have convergence of order one and two under appropriate regularity conditions.Keywords
All Related Versions
This publication has 17 references indexed in Scilit:
- Cubature methods for stochastic (partial) differential equations in weighted spacesStochastics and Partial Differential Equations: Analysis and Computations, 2013
- Mean field forward-backward stochastic differential equationsElectronic Communications in Probability, 2013
- Probabilistic Analysis of Mean-Field GamesSIAM Journal on Control and Optimization, 2013
- Sharp derivative bounds for solutions of degenerate semi-linear partial differential equationsJournal of Functional Analysis, 2012
- Numerical simulation of BSDEs with drivers of quadratic growthThe Annals of Applied Probability, 2011
- Continuous-time Stochastic Control and Optimization with Financial Applications2009
- Controlled Markov Processes and Viscosity Solutions2006
- Representation theorems for backward stochastic differential equationsThe Annals of Applied Probability, 2002
- Rate of convergence of a particle method to the solution of the McKean--Vlasov equationThe Annals of Applied Probability, 2002
- Classes of solutions of linear systems of partial differential equations of parabolic typeDuke Mathematical Journal, 1957