Unbiased Monte Carlo estimate of stochastic differential equations expectations
Doumbia, Mahamadou1 ; Oudjane, Nadia1 ; Warin, Xavier1
1 EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie (www.fime-lab.org), 7 boulevard Gaspard Monge, 91120 Palaiseau, France.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 56-87.

We propose an unbiased Monte Carlo method to compute E(g(X T )) where g is a Lipschitz function and X an Ito process. This approach extends the method proposed in [16] to the case where X is solution of a multidimensional stochastic differential equation with varying drift and diffusion coefficients. A variance reduction method relying on interacting particle systems is also developed.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2017001
Classification : 65C05, 60J60, 60J85, 35K10
Mots-clés : Unbiased estimate, linear parabolic PDEs, interacting particle systems
Doumbia, Mahamadou 1 ; Oudjane, Nadia 1 ; Warin, Xavier 1

1 EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie (www.fime-lab.org), 7 boulevard Gaspard Monge, 91120 Palaiseau, France. 
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     title = {Unbiased {Monte} {Carlo} estimate of stochastic differential equations expectations},
     journal = {ESAIM: Probability and Statistics},
     pages = {56--87},
     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/articles/10.1051/ps/2017001/}
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Doumbia, Mahamadou; Oudjane, Nadia; Warin, Xavier. Unbiased Monte Carlo estimate of stochastic differential equations expectations. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 56-87. doi : 10.1051/ps/2017001. http://www.numdam.org/articles/10.1051/ps/2017001/

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