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An improved simulation method for pricing high-dimensional American derivatives

Boyle, Phelim P.; Kolkiewicz, Adam W.; Tan, Ken Seng - In: Mathematics and Computers in Simulation (MATCOM) 62 (2003) 3, pp. 315-322

its upper bias converges to zero. An advantage of the proposed estimator is that when combined with low discrepancy …

Persistent link: https://www.econbiz.de/10010748767

On selection criteria for lattice rules and other quasi-Monte Carlo point sets

Lemieux, Christiane; L’Ecuyer, Pierre - In: Mathematics and Computers in Simulation (MATCOM) 55 (2001) 1, pp. 139-148

-stationarity of certain lattice rules, and of other low-discrepancy point sets sharing this property. Numerical results illustrate the …

Persistent link: https://www.econbiz.de/10010749493

A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems

Schürer, Rudolf - In: Mathematics and Computers in Simulation (MATCOM) 62 (2003) 3, pp. 509-517

Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared...

Persistent link: https://www.econbiz.de/10011050756

Numerical analysis of Jacobi series – A quasi-Monte-Carlo approach

Tichy, Robert F. - In: Mathematics and Computers in Simulation (MATCOM) 47 (1998) 2, pp. 473-481

Fourier coefficients for multivariate Jacobi series are computed by means of low-discrepancy sequences. Error bounds … are given in terms of discrepancy. …

Persistent link: https://www.econbiz.de/10010748679

Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space

El Haddad, R.; Lécot, C.; L’Ecuyer, P.; Nassif, N. - In: Mathematics and Computers in Simulation (MATCOM) 81 (2010) 3, pp. 560-567

We describe a quasi-Monte Carlo method for the simulation of discrete time Markov chains with continuous multi-dimensional state space. The method simulates copies of the chain in parallel. At each step the copies are reordered according to their successive coordinates. We prove the convergence...

Persistent link: https://www.econbiz.de/10010749210

Quasi-randomized numerical methods for systems with coefficients of bounded variation

Lécot, Christian - In: Mathematics and Computers in Simulation (MATCOM) 55 (2001) 1, pp. 113-121

bounds are derived which involve powers of the step size as well as the discrepancy of the point set used for quasi …

Persistent link: https://www.econbiz.de/10011050349

Simulation of diffusion using quasi-random walk methods

Coulibaly, Ibrahim; Lécot, Christian - In: Mathematics and Computers in Simulation (MATCOM) 47 (1998) 2, pp. 153-163

element in successfully applying the low discrepancy sequence is a technique involving renumbering the particles at each time …

Persistent link: https://www.econbiz.de/10011050578

Particle approximation of convection–diffusion equations

Lécot, Christian; Schmid, Wolfgang Ch. - In: Mathematics and Computers in Simulation (MATCOM) 55 (2001) 1, pp. 123-130

We present a particle method for solving initial-value problems for convection–diffusion equations with constant diffusion coefficients. We sample N particles at locations xj(0) from the initial data. We discretize time into intervals of length Δt. We represent the solution at time tn=nΔt by...

Persistent link: https://www.econbiz.de/10011050837

Constructing a new class of low-discrepancy sequences by using the β-adic transformation

Ninomiya, Syoiti - In: Mathematics and Computers in Simulation (MATCOM) 47 (1998) 2, pp. 403-418

It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods … [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical … generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the …

Persistent link: https://www.econbiz.de/10011051098

An adaptive approach to cube-based quasi-Monte Carlo integration on Rd

Pillards, Tim; Vandewoestyne, Bart; Cools, Ronald - In: Mathematics and Computers in Simulation (MATCOM) 80 (2010) 6, pp. 1104-1117

The standard domain for quasi-Monte Carlo approximations is the unit cube. Recently, much research has been done to make quasi-Monte Carlo methods applicable to the real space. Mathé and Wei proposed an algorithm that splits Rd into cubes. One of the difficulties with their approach is that the...

Persistent link: https://www.econbiz.de/10010870341