creator Li, Yao advisor Hickernell, Fred J. This research's purpose is to optimize an existing method to simulate stochas- tic integrals using Monte Carlo when the cost of function evaluation is dimension dependent. In the area of mathematical nance, we often need to price a path- dependent nancial derivative. This will result in the computation of E[g(B( ))], where g stands for a payoff function, and B is the Brownian Motion. A simple way to approximate this expectation is to take the average of the functional over a large num- ber of sample paths. Each path is approximated by a d-dimensional random vector. A larger d will provide a more accurate result. However, due to the limitation in time cost and computer memory, some large dimensions are not easy to be implemented. Therefore, we introduce the multi-level technique that is based on multi-grid ideas. It can be used to reduce the computational complexity for these kind of problems. Moreover, when we apply the multi-level technique, the proper sample size for each subspace integration needs to be computed in order to satisfy our guaranteed conser- vative xed width con dence intervals. Thus, the automatic sample size algorithm (two stage con dence interval algorithm) is used in conjunction with the multi-level method. Submitted by Liana Khananashvili (khananashvili@iit.edu) on 2014-05-08T17:09:20Z No. of bitstreams: 2 Yao Li thesis Multilevel Monte Carlo Based on the Autometic Sample Size Algorithm.pdf: 1531424 bytes, checksum: 0c7fc4e83b42c5b9d297e8c27cd12923 (MD5) Signed title page.pdf: 100730 bytes, checksum: 090622d005c5d2774565c8c5e730cd15 (MD5) Made available in DSpace on 2014-05-08T17:09:20Z (GMT). No. of bitstreams: 2 Yao Li thesis Multilevel Monte Carlo Based on the Autometic Sample Size Algorithm.pdf: 1531424 bytes, checksum: 0c7fc4e83b42c5b9d297e8c27cd12923 (MD5) Signed title page.pdf: 100730 bytes, checksum: 090622d005c5d2774565c8c5e730cd15 (MD5) Previous issue date: 2013-12 M.S. in Applied Mathematics, December 2013 2013 2013-12 http://hdl.handle.net/10560/3216 en Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department