Monte Carlo and Quasi-Monte Carlo Methods 2002: Proceedings by Phelim P. Boyle (auth.), Harald Niederreiter (eds.)

By Phelim P. Boyle (auth.), Harald Niederreiter (eds.)

This ebook represents the refereed lawsuits of the 5th overseas convention on Monte Carlo and Quasi-Monte Carlo equipment in medical Computing which was once held on the nationwide collage of Singapore within the yr 2002. a big characteristic are invited surveys of the state-of-the-art in key components comparable to multidimensional numerical integration, low-discrepancy aspect units, computational complexity, finance, and different purposes of Monte Carlo and quasi-Monte Carlo equipment. those lawsuits additionally comprise conscientiously chosen contributed papers on all features of Monte Carlo and quasi-Monte Carlo tools. The reader may be proficient approximately present examine during this very energetic area.

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Additional resources for Monte Carlo and Quasi-Monte Carlo Methods 2002: Proceedings of a Conference held at the National University of Singapore, Republic of Singapore, November 25–28, 2002

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For fixed x E {a, 1, . , N - I} the probability of getting x as output is obviously 1 28 + 28 N21 + (2-2- N) 2 8 - 8 8 - 8- 2 1 28 + ... = 1 28 (2 8 ~ -2-800 N) i 1 = N' Hence the above procedure implements indeed uniform sampling from the set {O, 1, . . , N - I}. How many random bits on the average are necessary to Monte Carlo with Few Random Bits 35 realize an element of {O, 1, . , N - I} according to the uniform distribution? Clearly, this number equals N s-8 + 2s 2 28 N N 8 2 28 + 3s (2- -_ -N ) 2 -N + ...

Under the standard Black Scholes assumptions the price of a standard European option has a closed form solution. This is not the case with the corresponding American option. However the partial differential equation can be solved numerically for the price of the American option and this was done by Schwartz in his doctoral thesis in 1975. He used a finite difference approach to solve the differential equation for the American option. The contracts considered by Merton and Schwartz were American options based on a single underlying asset.

Remark 1. a) The error of all four methods is similar if n is much smaller than N. The cost of A~ and A; is about n· (c + 10gN), the cost of A~ and A~ is only about en + log N . b) Concerning A~ and A~ we mention that the classical Monte Carlo method is based on the fact that we use pairwise independent indices, a "complete" independence is not needed. It is not difficult to prove the following. Let N E N, and let Xl and X 2 be independent and on the set {O,I, . , N -I} equidistributed random variables.

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