# Monte Carlo and Quasi-Monte Carlo Sampling

Springer Science & Business Media, 03.04.2009 - 373 Seiten

Quasi-Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute.

This book presents essential tools for using quasi-Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi-random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi-Monte Carlo counterpart.

The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi-Monte Carlo methods and researchers interested in an up-to-date guide to these methods.

Christiane Lemieux is an Associate Professor and the Associate Chair for Actuarial Science in the Department of Statistics and Actuarial Science at the University of Waterloo in Canada. She is an Associate of the Society of Actuaries and was the winner of a “Young Researcher Award in Information-Based Complexity” in 2004.

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### Inhalt

 I 1 II 3 III 12 IV 20 V 22 VI 25 VII 27 VIII 34
 XLIX 174 L 179 LI 180 LII 187 LIII 197 LV 200 LVI 202 LVII 204

 IX 41 X 42 XI 44 XII 46 XIII 48 XIV 50 XV 51 XVI 55 XVII 57 XVIII 58 XIX 60 XX 61 XXI 64 XXII 66 XXIII 67 XXIV 68 XXV 70 XXVI 75 XXVII 80 XXVIII 85 XXIX 87 XXX 89 XXXII 101 XXXIII 111 XXXIV 119 XXXV 125 XXXVI 132 XXXVII 135 XXXVIII 136 XXXIX 137 XL 139 XLI 143 XLII 146 XLIII 153 XLIV 157 XLV 161 XLVI 163 XLVII 164 XLVIII 170
 LVIII 206 LX 209 LXI 210 LXII 211 LXIII 214 LXIV 216 LXV 222 LXVI 225 LXVII 228 LXVIII 229 LXIX 237 LXX 239 LXXI 241 LXXII 247 LXXIV 256 LXXV 257 LXXVI 258 LXXVII 260 LXXIX 273 LXXXII 275 LXXXIII 279 LXXXIV 281 LXXXV 282 LXXXVI 283 LXXXVII 288 LXXXVIII 298 LXXXIX 301 XC 303 XCI 305 XCII 310 XCIII 312 XCIV 320 XCV 332 XCVI 335 XCVII 341 XCVIII 347 XCIX 369 Urheberrecht

### Über den Autor (2009)

Christiane Lemieux is an Associate Professor and the Associate Chair for Actuarial Science in the Department of Statistics and Actuarial Science at the University of Waterloo in Canada. She is an Associate of the Society of Actuaries and was the winner of a “Young Researcher Award in Information-Based Complexity” in 2004.