Simulation of McKean-Vlasov BSDEs by Wiener chaos expansion
Résumé
We present an algorithm to solve McKean-Vlasov BSDEs based on Wiener chaos expansion and Picard's iterations and study its convergence. This paper extends the results obtained by Briand and Labart in [BL14] when standard BSDEs were considered. Here we are faced with the problem of the approximation of the law of (Y, Z) in the driver, that we solve by using a particle system. In order to avoid solving a system of BSDEs, which would not be feasible in practice, we use the same particles to approximate the law of (Y, Z) and to compute Monte Carlo approximations. This leads to an algorithm which doesn't cost more than the standard one.
Domaines
Probabilités [math.PR]
Fichier principal
article_2019_01_09.pdf (672.86 Ko)
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erreur_M(f=Y+E(Z),xi=B_T^2,M=10^3..10^6,N=20,L=10,p=2,q=6).jpg (14.25 Ko)
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evolution_Y(p=3,xi=sqrt B_T,N=20,f=Y+E(Z))_codeCeline.jpg (17.16 Ko)
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evolution_Y_M_loi(N=20,f=Y+E(Z),xi=B_T^2).jpg (17.96 Ko)
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evolution_Z(p=3,xi=sqrt B_T,N=20,f=Y+E(Z))_codeCeline.jpg (19.43 Ko)
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evolution_Z_M_loi(N=20,f=Y+E(Z),xi=B_T^2).jpg (18.1 Ko)
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evolution_wrt_p3_q_N_Y_codeCeline.jpg (16.54 Ko)
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evolution_wrt_p3_q_N_Z_codeCeline.jpg (15.52 Ko)
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