Correction to “Quasi-Monte Carlo methods for high-dimensional integration: the standard (weighted Hilbert space) setting and beyond”

2013 ◽  
Vol 54 ◽  
pp. 216 ◽  
Author(s):  
F. Y. Kuo ◽  
Ch. Schwab ◽  
I. H. Sloan
Keyword(s):  
Hilbert Space ◽  
Monte Carlo ◽  
Monte Carlo Methods ◽  
High Dimensional ◽  
Quasi Monte Carlo ◽  
Space Setting

scholarly journals Comparison of Sobol’ sequences in financial applications

2019 ◽  
Vol 25 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Shin Harase
Keyword(s):  
Monte Carlo ◽  
Comparative Study ◽  
Monte Carlo Methods ◽  
Financial Models ◽  
Slight Modification ◽  
High Dimensional ◽  
Financial Applications ◽  
Quasi Monte Carlo ◽  
Parameter Values

Abstract Sobol’ sequences are widely used for quasi-Monte Carlo methods that arise in financial applications. Sobol’ sequences have parameter values called direction numbers, which are freely chosen by the user, so there are several implementations of Sobol’ sequence generators. The aim of this paper is to provide a comparative study of (non-commercial) high-dimensional Sobol’ sequences by calculating financial models. Additionally, we implement the Niederreiter sequence (in base 2) with a slight modification, that is, we reorder the rows of the generating matrices, and analyze and compare it with the Sobol’ sequences.

scholarly journals Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

2017 ◽  
Vol 86 (308) ◽  
pp. 2827-2860 ◽  
Author(s):  
Frances Y. Kuo ◽  
Robert Scheichl ◽  
Christoph Schwab ◽  
Ian H. Sloan ◽  
Elisabeth Ullmann
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Quasi Monte Carlo ◽  
Diffusion Problems
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