Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Quasi-Monte Carlo methods in numerical finance
Management Science
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Finite-order weights imply tractability of multivariate integration
Journal of Complexity
Derivatives and credit risk: enhanced quasi-monte carlo methods with dimension reduction
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
Efficient Weighted Lattice Rules with Applications to Finance
SIAM Journal on Scientific Computing
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
Constructing Robust Good Lattice Rules for Computational Finance
SIAM Journal on Scientific Computing
Low discrepancy sequences in high dimensions: How well are their projections distributed?
Journal of Computational and Applied Mathematics
New Brownian bridge construction in quasi-Monte Carlo methods for computational finance
Journal of Complexity
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
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Many problems in mathematical finance (e.g., the pricing of financial derivative securities) can be formulated as high-dimensional integrals, which are often tackled by quasi-Monte Carlo methods. Quasi-random points have the special property that the one-dimensional projections and the earlier dimensional projections are extremely well distributed. This property strongly motivates us to reduce the effective dimensions of the problems. This paper deals with multiasset path-dependent options. The goal of this paper is twofold: (1) to design new methods for dimension reduction and to offer further insight into dimension reduction techniques, and (2) to investigate the practical performance of various dimension reduction strategies in conjunction with different quasi-random points (digital nets and good lattice points). We propose two groups of two-stage procedures for the constructions of correlated multidimensional Brownian motions, which provide a general framework to combine and use different dimension reduction techniques and optimize the use of quasi-random points. We find the inherent weights that characterize the weighted property and the dimension structure of the underlying functions (e.g., the sensitivity indices, the effective dimensions, etc.), and show how each dimension reduction strategy affects them. Numerical experiments on multiasset path-dependent options demonstrate that significant improvements can be achieved by proper use of dimension reduction strategies and quasi-random points. It is also shown that different quasi-random point sets have different behavior with respect to dimension reduction strategies.