Monte Carlo and Quasi-Monte Carlo Methods 2008

Transcription

1 Monte Carlo and Quasi-Monte Carlo Methods 2008

2 Pierre L Ecuyer Art B. Owen Editors Monte Carlo and Quasi- Monte Carlo Methods 2008

3 Editors Pierre L Ecuyer DIRO Université de Montréal C.P. 6128, Succ. Centre-Ville Montreal, H3C 3J7 Canada lecuyer@iro.umontreal.ca Art B. Owen Department of Statistics Stanford University Sequoia Hall Stanford, CA USA owen@stanford.edu ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: Mathematics Subject Classification (2000): Primary 11K45, 65-06, 65C05, 65C10; Secondary 11K38, 65D18, 65D30, 65D32, 65R20, 91B28 Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: VTeX, Vilnius Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 Preface This volume represents the refereed proceedings of the Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, which was held at the University of Montréal, from 6 11 July, It contains a limited selection of articles based on presentations made at the conference. The program was arranged with the help of an international committee consisting of: Ronald Cools, Katholieke Universiteit Leuven Luc Devroye, McGill University Henri Faure, CNRS Marseille Paul Glasserman, Columbia University Peter W. Glynn, Stanford University Stefan Heinrich, University of Kaiserslautern Fred J. Hickernell, Illinois Institute of Technology Aneta Karaivanova, Bulgarian Academy of Science Alexander Keller, mental images GmbH, Berlin Adam Kolkiewicz, University of Waterloo Frances Y. Kuo, University of New South Wales Christian Lécot, Université de Savoie, Chambéry Pierre L Ecuyer, Université de Montréal (Chair and organizer) Jun Liu, Harvard University Peter Mathé, Weierstrass Institute Berlin Makoto Matsumoto, Hiroshima University Thomas Müller-Gronbach, Otto von Guericke Universität Harald Niederreiter, National University of Singapore Art B. Owen, Stanford University Gilles Pagès, Université Pierre et Marie Curie (Paris 6) Klaus Ritter, TU Darmstadt Karl Sabelfeld, Weierstrass Institute Berlin Wolfgang Ch. Schmid, University of Salzburg Ian H. Sloan, University of New South Wales Jerome Spanier, University of California, Irvine Bruno Tuffin, IRISA-INRIA, Rennes Henryk Woźniakowski, Columbia University. v

5 vi Preface The local arrangements (program production, publicity, web site, registration, social events, etc.) were ably handled by Carole Dufour (GERAD), Marilyne Lavoie (GERAD), Louis Pelletier (CRM), Marie Perreault (GERAD), and Suzette Paradis (CRM). Francine Benoit (GERAD) helped with editing the proceedings. This conference continued the tradition of biennial MCQMC conferences initiated by Harald Niederreiter. They were begun at the University of Nevada in Las Vegas, Nevada, USA, in June 1994 and followed by conferences at the University of Salzburg, Austria, in July 1996, the Claremont Colleges in Claremont, California, USA, in June 1998, Hong Kong Baptist University in Hong Kong, China, in November 2000, the National University of Singapore, Republic of Singapore, in November 2002, the Palais des Congrès in Juan-les-Pins, France, in June 2004, and Ulm University, Germany, in July The next MCQMC conference will be held in Warsaw, Poland, in August The proceedings of these previous conferences were all published by Springer- Verlag, under the following titles: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P.J.-S. Shiue, eds.), Monte Carlo and Quasi-Monte Carlo Methods 1996 (H. Niederreiter, P. Hellekalek, G. Larcher and P. Zinterhof, eds.), Monte Carlo and Quasi-Monte Carlo Methods 1998 (H. Niederreiter and J. Spanier, eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000 (K.-T. Fang, F.J. Hickernell and H. Niederreiter, eds.), Monte Carlo and Quasi-Monte Carlo Methods 2002 (H. Niederreiter, ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004 (H. Niederreiter and D. Talay, eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006 (A. Keller and S. Heinrich and H. Niederreiter, eds.). The program of the conference was rich and varied with over 135 talks being presented. Highlights were the invited plenary talks given by Josef Dick (University of New South Wales), Arnaud Doucet (University of British Columbia), Daan Frenkel (University of Cambridge), Paul Glasserman (Columbia University), Christiane Lemieux (University of Waterloo), Jun Liu (Harvard University), Klaus Ritter (TU Darmstadt), Jeffrey Rosenthal (University of Toronto), Wolfgang Schmid (University of Salzburg), and Andrew Stuart (Warwick University). The papers in this volume were carefully screened and cover both the theory and the applications of Monte Carlo and quasi-monte Carlo methods. We thank the anonymous reviewers for their reports and many others who contributed enormously to the excellent quality of the conference presentations and to the high standards for publication in these proceedings by careful review of the abstracts and manuscripts that were submitted. We gratefully acknowledge generous financial support of the conference by the Centre de Recherches Mathématiques (CRM), the Groupe d Études et de Recherche en Analyse de Décisions (GERAD), Mathematics for Information Technology

6 Preface vii and Complex Systems (MITACS), and the American National Science Foundation (NSF). Finally, we want to express our gratitude to Springer-Verlag for publishing this volume. July 2009 Pierre L Ecuyer Art Owen

7 Contents Part I Tutorials Monte Carlo and Quasi-Monte Carlo for Statistics... 3 Art B. Owen Monte Carlo Computation in Finance Jeremy Staum Part II Invited Articles Particle Markov Chain Monte Carlo for Efficient Numerical Simulation. 45 Christophe Andrieu, Arnaud Doucet, and Roman Holenstein Computational Complexity of Metropolis-Hastings Methods in High Dimensions Alexandros Beskos and Andrew Stuart On Quasi-Monte Carlo Rules Achieving Higher Order Convergence Josef Dick Sensitivity Estimates for Compound Sums Paul Glasserman and Kyoung-Kuk Kim New Perspectives on (0,s)-Sequences Christiane Lemieux and Henri Faure Variable Subspace Sampling and Multi-level Algorithms Thomas Müller-Gronbach and Klaus Ritter Markov Chain Monte Carlo Algorithms: Theory and Practice Jeffrey S. Rosenthal ix

8 x Contents MINT New Features and New Results Rudolf Schürer and Wolfgang Ch. Schmid Part III Contributed Articles Recursive Computation of Value-at-Risk and Conditional Value-at-Risk using MC and QMC Olivier Bardou, Noufel Frikha, and Gilles Pagès Adaptive Monte Carlo Algorithms Applied to Heterogeneous Transport Problems Katherine Bhan, Rong Kong, and Jerome Spanier Efficient Simulation of Light-Tailed Sums: an Old-Folk Song Sung to a Faster New Tune Jose H. Blanchet, Kevin Leder, and Peter W. Glynn Distribution of Digital Explicit Inversive Pseudorandom Numbers and Their Binary Threshold Sequence Zhixiong Chen, Domingo Gomez, and Arne Winterhof Extensions of Fibonacci Lattice Rules Ronald Cools and Dirk Nuyens Efficient Search for Two-Dimensional Rank-1 Lattices with Applications in Graphics Sabrina Dammertz, Holger Dammertz, and Alexander Keller Parallel Random Number Generators Based on Large Order Multiple Recursive Generators Lih-Yuan Deng, Jyh-Jen Horng Shiau, and Gwei-Hung Tsai Efficient Numerical Inversion for Financial Simulations Gerhard Derflinger, Wolfgang Hörmann, Josef Leydold, and Halis Sak Equidistribution Properties of Generalized Nets and Sequences Josef Dick and Jan Baldeaux Implementation of a Component-By-Component Algorithm to Generate Small Low-Discrepancy Samples Benjamin Doerr, Michael Gnewuch, and Magnus Wahlström Quasi-Monte Carlo Simulation of Diffusion in a Spatially Nonhomogeneous Medium Rami El Haddad, Christian Lécot, and Gopalakrishnan Venkiteswaran L 2 Discrepancy of Two-Dimensional Digitally Shifted Hammersley Point Sets in Base b Henri Faure and Friedrich Pillichshammer

9 Contents xi Vibrato Monte Carlo Sensitivities Michael B. Giles The Weighted Variance Minimization in Jump-Diffusion Stochastic Volatility Models Anatoly Gormin and Yuri Kashtanov (t,m,s)-nets and Maximized Minimum Distance, Part II Leonhard Grünschloß and Alexander Keller Automation of Statistical Tests on Randomness to Obtain Clearer Conclusion Hiroshi Haramoto On Subsequences of Niederreiter-Halton Sequences Roswitha Hofer Correcting the Bias in Monte Carlo Estimators of American-style Option Values K.H. Felix Kan, R. Mark Reesor, Tyson Whitehead, and Matt Davison Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps Jens Keiner and Benjamin J. Waterhouse Adaptive Monte Carlo Algorithms for General Transport Problems Rong Kong, Martin Ambrose, and Jerome Spanier On Array-RQMC for Markov Chains: Mapping Alternatives and Convergence Rates Pierre L Ecuyer, Christian Lécot, and Adam L Archevêque-Gaudet Testing the Tests: Using Random Number Generators to Improve Empirical Tests Paul Leopardi Stochastic Spectral Formulations for Elliptic Problems Sylvain Maire and Etienne Tanré Adaptive (Quasi-)Monte Carlo Methods for Pricing Path-Dependent Options Roman N. Makarov Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent Ben Niu and Fred J. Hickernell

10 xii Contents Recent Progress in Improvement of Extreme Discrepancy and Star Discrepancy of One-Dimensional Sequences Victor Ostromoukhov Discrepancy of Hyperplane Nets and Cyclic Nets Friedrich Pillichshammer and Gottlieb Pirsic A PRNG Specialized in Double Precision Floating Point Numbers Using an Affine Transition Mutsuo Saito and Makoto Matsumoto On the Behavior of the Weighted Star Discrepancy Bounds for Shifted Lattice Rules Vasile Sinescu and Pierre L Ecuyer Ergodic Estimations of Upscaled Coefficients for Diffusion in Random Velocity Fields Nicolae Suciu and Călin Vamoş Green s Functions by Monte Carlo David White and Andrew Stuart Tractability of Multivariate Integration for Weighted Korobov Spaces: My 15 Year Partnership with Ian Sloan Henryk Woźniakowski Conference Participants Index...671