TY - JOUR
T1 - Sequential Monte Carlo methods for diffusion processes
AU - Jasra, Ajay
AU - Doucet, Arnaud
N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20
PY - 2009/12/8
Y1 - 2009/12/8
N2 - In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high-and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging. © 2009 The Royal Society.
AB - In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high-and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging. © 2009 The Royal Society.
UR - https://royalsocietypublishing.org/doi/10.1098/rspa.2009.0206
UR - http://www.scopus.com/inward/record.url?scp=73149085475&partnerID=8YFLogxK
U2 - 10.1098/rspa.2009.0206
DO - 10.1098/rspa.2009.0206
M3 - Article
SN - 1471-2946
VL - 465
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2112
ER -