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

[21] MONTE CARLO SIMULATIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS AT THE EXAMPLE OF THE FORCED BURGERS' EQUATION
Homeier, D.
Jansen, K.
Mesterhazy, D.
Urbach, C.
PATH INTEGRALS: NEW TRENDS AND PERSPECTIVES, PROCEEDINGS, 2008, : 346 - +
[22] DIVERGENCE OF THE MULTILEVEL MONTE CARLO EULER METHOD FOR NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
Hutzenthaler, Martin
Jentzen, Arnulf
Kloeden, Peter E.
ANNALS OF APPLIED PROBABILITY, 2013, 23 (05): : 1913 - 1966
[23] Stochastic differential equations for non-analog Monte Carlo model of point kinetics equations
Melikkendli, Behram
Tombakoglu, Mehmet
PROGRESS IN NUCLEAR ENERGY, 2024, 176
[24] UNBIASED MONTE CARLO COMPUTATION OF SMOOTH FUNCTIONS OF EXPECTATIONS VIA TAYLOR EXPANSIONS
Blanchet, Jose H.
Chen, Nan
Glynn, Peter W.
2015 WINTER SIMULATION CONFERENCE (WSC), 2015, : 360 - 367
[25] A regression-based Monte Carlo method to solve backward stochastic differential equations
Gobet, E
Lemor, JP
Warin, X
ANNALS OF APPLIED PROBABILITY, 2005, 15 (03): : 2172 - 2202
[26] FINITE VARIANCE UNBIASED ESTIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS
Agarwal, Ankush
Gobet, Emmanuel
2017 WINTER SIMULATION CONFERENCE (WSC), 2017, : 1950 - 1961
[27] A MICRO-MACRO ACCELERATION METHOD FOR THE MONTE CARLO SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS
Debrabant, Kristian
Samaey, Giovanni
Zielinski, Przemyslaw
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (06) : 2745 - 2786
[28] MONTE-CARLO-TYPE SIMULATION FOR SOLVING STOCHASTIC ORDINARY DIFFERENTIAL-EQUATIONS
SPIGLER, R
MATHEMATICS AND COMPUTERS IN SIMULATION, 1987, 29 (3-4) : 243 - 251
[29] A class of stochastic differential equations with expectations in the coefficients
Hu, Yangzi
Wu, Fuke
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 81 : 190 - 199
[30] UNBIASED MONTE CARLO FOR OPTIMIZATION AND FUNCTIONS OF EXPECTATIONS VIA MULTI-LEVEL RANDOMIZATION
Blanchet, Jose H.
Glynn, Peter W.
2015 WINTER SIMULATION CONFERENCE (WSC), 2015, : 3656 - 3667

← 1 2 3 4 5 →