Name
Abstract | ||
|---|---|---|
We show how simple kinks and jumps of otherwise smooth integrands over Rd can be dealt with by a preliminary integration with respect to a single well chosen variable. It is assumed that this preintegration, or conditional sampling, can be carried out with negligible error, which is the case in particular for option pricing problems. It is proven that under appropriate conditions the preintegrated function of d−1 variables belongs to appropriate mixed Sobolev spaces, so potentially allowing high efficiency of Quasi Monte Carlo and Sparse Grid Methods applied to the preintegrated problem. The efficiency of applying Quasi Monte Carlo to the preintegrated function are demonstrated on a digital Asian option using the Principal Component Analysis factorization of the covariance matrix. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2018.04.009 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
High dimensional integration,Smoothing,Preintegration,ANOVA decomposition,Quasi Monte Carlo,Conditional sampling | Applied mathematics,Valuation of options,Mathematical analysis,Sobolev space,Quasi-Monte Carlo method,Smoothing,Asian option,Covariance matrix,Sparse grid,Principal component analysis,Mathematics | Journal |
Volume | ISSN | Citations |
344 | 0377-0427 | 0 |
PageRank | References | Authors |
0.34 | 6 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andreas Griewank | 1 | 526 | 110.14 |
| Frances Y. Kuo | 2 | 479 | 45.19 |
| H. Leovey | 3 | 11 | 3.16 |
| Ian H. Sloan | 4 | 1180 | 183.02 |