By Art B. Owen (auth.), Pierre L' Ecuyer, Art B. Owen (eds.)
This ebook represents the refereed court cases of the 8th foreign convention on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) tools in medical Computing, held in Montreal (Canada) in July 2008. It covers the most recent theoretical advancements in addition to vital functions of those equipment in several parts. It includes tutorials, 8 invited articles, and 32 rigorously chosen articles in keeping with the one hundred thirty five contributed shows made on the convention. This convention is a massive occasion in Monte Carlo equipment and is the prime occasion for quasi-Monte Carlo and its blend with Monte Carlo. This sequence of complaints volumes is the first outlet for quasi-Monte Carlo research.
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Extra resources for Monte Carlo and Quasi-Monte Carlo Methods 2008
The objective is often to maximize the expected utility E[u(W (T ))] of future wealth W (T ) = θ(T ) S(T ), or to maximize the expected −βti u(C(t ))] of a consumption process C, which total discounted utility E[ m i i=0 e is another decision variable. The investor’s initial wealth W (0) imposes the budget constraint θ S(0) = W (0). A multi-period formulation requires self-financing constraints like θ (ti ) S(ti ) = θ (ti−1 ) S(ti ) − C(ti ), which may be more complicated if there are features such as transaction costs and taxes.
Nelson, and Jeremy Staum. Stochastic kriging for simulation metamodeling. Operations Research. Forthcoming. 4. Bouhari Arouna. Adaptative Monte Carlo method, a variance reduction technique. Monte Carlo Methods and Applications, 10(1):1–24, 2004. 5. Søren Asmussen and Jan Rosi´nski. Approximations of small jumps of L´evy processes with a view towards simulation. Journal of Applied Probability, 38(2):482–493, 2001. 6. Athanassios N. Avramidis and Pierre L’Ecuyer. Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance-gamma model.
The method of weak derivatives (WD) can be explained based on LR : suppose ∂g(x; θ )/∂θ can be written in the form c(θ )(g1 (x; θ ) − g2 (x; θ )), where g1 (·; θ ) and g2 (·; θ ) are densities. If the LR approach is valid, then μ (θ ) = c(θ ) f˜(x)g1 (x; θ ) dx − = c(θ )E f˜(X1 ) − f˜(X2 ) , f˜(x)g2 (x; θ ) dx 36 Jeremy Staum where X1 and X2 are sampled according to the densities g1 (·; θ ) and g2 (·; θ ) respectively: an unbiased estimator is c(θ )(f˜(X1 ) − f˜(X2 )). ) Here we did not specify how the original pseudo-random numbers would be used to simulate X1 and X2 .
Monte Carlo and Quasi-Monte Carlo Methods 2008 by Art B. Owen (auth.), Pierre L' Ecuyer, Art B. Owen (eds.)