Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Average case complexity of multivariate integration for smooth functions
Journal of Complexity
The exponent of discrepancy is at most 1.4778…
Mathematics of Computation
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
Faster evaluation of multidimensional integrals
Computers in Physics
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
On the L2-discrepancy for anchored boxes
Journal of Complexity
Complexity and information
Fast convergence of quasi-Monte Carlo for a class of isotropic integrals
Mathematics of Computation
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places
Finite Fields and Their Applications
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In this paper, we first give a brief overview of discrepancy theory, then introduce low-discrepancy sequences, in particular, the original Faure and generalized Faure sequences. Next, we describe how to apply them to the problem of pricing financial derivatives, along with a successful application of this technique to the valuation of the present value of mortgage-backed securities (MBS). Finally, we will discuss future research directions.