An empirical study of the efficiency of EA for diffusion simulation
Peluchetti, Stefano and Roberts, Gareth O. (2008) An empirical study of the efficiency of EA for diffusion simulation. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
WRAP_Pelcuhetti_08-14w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
In this paper we investigate the efficiency of some simulation schemes for the numerical solution of a one dimensional stochastic differential equation (SDE). The schemes considered are: the Exact Algorithm (EA), the Euler, the Predictor-Corrector and the Ozaki- Shoji schemes. The focus of the work is on EA which samples skeletons of SDEs without any approximation. The analysis is carried out via a simulation study using some test SDEs. We also consider efficiency issues arising by the extension of EA to the multi-dimensional setting.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Stochastic differential equations, Diffusion processes|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||26|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Y. Ait-Sahalia. Closed-Form Likelihood Expansions for Multivariate Diffusions. 2002. C. Albanese and A. Kuznetsov. Transformations of Markov processes and classification scheme for solvable driftless diffusions. preprint, www3. imperial. ac. uk/mathfin/people/calban/papersmathfin, 2005. A. Beskos and G.O. Roberts. Exact simulation of diffusions. Ann. Appl. Probab, 15:2422- 2444, 2005. A. Beskos, O. Papaspiliopoulos, and G.O. Roberts. Retrospective exact simulation of diffusion sample paths with applications. Bernoulli, 12:1077-1098, 2006a. A. Beskos, O. Papaspiliopoulos, and G.O. Roberts. A new factorisation of diffusion measure and finite sample path construction. Methodology and Computing in Applied Probability, Submitted, 2006b. Bruno Casella. Exact MC simulation for diffusion and jump-diffusion processes with financial applications. PhD thesis, IMQ - Bocconi University, 2005. WR Gilks. Derivative-free adaptive rejection sampling for Gibbs sampling. Bayesian Statis- tics, 4(2):641-649, 1992. WR Gilks and P. Wild. Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics, 41(2):337-348, 1992. P.E. Kloeden and E. Platen. Numerical Solution of Stochastic Differential Equations. Springer, 1992. G. Maruyama. Continuous markov processes and stochastic equations. Rend. Circ. Mat. Palermo, 4:48-90, 1955. Stefano Peluchetti. An analysis of the efficiency of the Exact Algorithm. PhD thesis, IMQ - Universitá Commerciale Luigi Bocconi, 2007. I. Shoji and T. Ozaki. Estimation for nonlinear stochastic differential equations by a local linearization method. Stochastic Analysis and Applications, 16(4):733-752, 1998.|
Actions (login required)