UNBIASED MONTE CARLO ESTIMATE OF STOCHASTIC DIFFERENTIAL EQUATIONS EXPECTATIONS

被引：8

作者：

Doumbia, Mahamadou ^{[1
,2
]}

Oudjane, Nadia ^{[1
,2
]}

Warin, Xavier ^{[1
,2
]}

机构：

[1] EDF R&D, 7 Blvd Gaspard Monge, F-91120 Palaiseau, France

[2] FiME, Lab Finance Marches Energie, 7 Blvd Gaspard Monge, F-91120 Palaiseau, France

来源：

ESAIM-PROBABILITY AND STATISTICS | 2017年 / 21卷

关键词：

Unbiased estimate; linear parabolic PDEs; interacting particle systems; EXACT SIMULATION;

D O I：

10.1051/ps/2017001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：56 / 87

页数：32

共 50 条

[1] Estimating the parameters of stochastic differential equations by Monte Carlo methods
Hurn, AS
Lindsay, KA
MATHEMATICS AND COMPUTERS IN SIMULATION, 1997, 43 (3-6) : 495 - 501
[2] MULTILEVEL MONTE CARLO FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH SMALL NOISE
Anderson, David F.
Higham, Desmond J.
Sun, Yu
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (02) : 505 - 529
[3] On quasi-Monte Carlo simulation of stochastic differential equations
Hofmann, N
Mathe, P
MATHEMATICS OF COMPUTATION, 1997, 66 (218) : 573 - 589
[4] UNBIASED SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS
Henry-Labordere, Pierre
Tan, Xiaolu
Touzi, Nizar
ANNALS OF APPLIED PROBABILITY, 2017, 27 (06): : 3305 - 3341
[5] Multilevel Monte Carlo for stochastic differential equations with additive fractional noise
Peter E. Kloeden
Andreas Neuenkirch
Raffaella Pavani
Annals of Operations Research, 2011, 189 : 255 - 276
[6] Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Barth, Andrea
Lang, Annika
Schwab, Christoph
BIT NUMERICAL MATHEMATICS, 2013, 53 (01) : 3 - 27
[7] On a Monte Carlo scheme for some linear stochastic partial differential equations
Nakagawa, Takuya
Tanaka, Akihiro
MONTE CARLO METHODS AND APPLICATIONS, 2021, 27 (02): : 169 - 193
[8] Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Andrea Barth
Annika Lang
Christoph Schwab
BIT Numerical Mathematics, 2013, 53 : 3 - 27
[9] Multilevel Monte Carlo for stochastic differential equations with additive fractional noise
Kloeden, Peter E.
Neuenkirch, Andreas
Pavani, Raffaella
ANNALS OF OPERATIONS RESEARCH, 2011, 189 (01) : 255 - 276
[10] Multilevel Monte Carlo method with applications to stochastic partial differential equations
Barth, Andrea
Lang, Annika
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2012, 89 (18) : 2479 - 2498

← 1 2 3 4 5 →