This paper discusses European style option pricing for both path dependent and nonpath dependent cases where the log returns of the underlying asset follow the normal inverse Gaussian (NIG) distributions. The moment matching method is used in estimating ...

Direction numbers for generating Sobol$'$ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49-57]. However, these Sobol$'$ sequences ...

In this paper we introduce the intermediate rank or higher rank lattice rule for the general case when the number of quadrature points is n^tm, where m is a composite integer, t is the rank of the rule, n is an integer ...

A model function f(x"1,...,x"n) defined in the unit hypercube H^n with Lebesque measure dx=dx"1...dx"n is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors ...

A number of features relevant to stochastic dynamical systems, such as moments of solutions and first passage times, can be efficiently computed resorting to sequences of quasi-random numbers (low-discrepancy sequences). This method represents an alternative ...

We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference ...

In this paper, we give explicit constructions of point sets in the $s$-dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high-dimensional periodic ...

Quasi-Monte Carlo (QMC) methods have been successfully used to compute high-dimensional integrals arising in many applications, especially in finance. To understand the success and the potential limitation of QMC, this paper focuses on quality measures ...

Existence theorems for good parameters in a construction of low-discrepancy point sets based on rational functions over finite fields are proved. A special class of these point sets is introduced and good parameters in the construction of these special ...

In this paper various measures for the uniformity of distribution of a point set in the unit cube are studied. We show how the diaphony and spectral test based on Walsh functions appear naturally as the worst-case error of integration in certain Hilbert ...

A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation ...

A quasi-Monte Carlo particle simulation for solving a linear Boltzmann equation is constructed and a convergence proof is given. The analysis is restricted to the three-dimensional equation in the space homogeneous case and the velocity domain is normalized ...

In contrast to random points that may cluster, quasi-random points keep their distance. These distances are investigated.1.If N independent random points in the n-dimensional unit hypercube are selected, two of these points may be arbitrarily close. ...

The authors develop a new Monte Carlo-based method for pricing path-dependent options under the variance gamma (VG) model. The gamma bridge sampling method proposed by Avramidis et al. (Avramidis, A. N., P. L'Ecuyer, P. A. Tremblay. 2003. Efficient simulation ...

In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. ...

This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to Monte Carlo ...

In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This ...