The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The aim of this review ...

Tournament outcome uncertainty depends on: the design of the tournament; and the relative strengths of the competitors – the competitive balance. A tournament design comprises the arrangement of the individual matches, which we call the tournament structure, the seeding policy and the progression rules. In this paper, we investigate the effect of seeding policy for various tournament structures...

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the perform...

Quasi-Monte Carlo is usually employed to speed up the convergence of Monte Carlo in approximating multivariate integrals. While convergence of the Monte Carlo method is O(N−1/2), that of plain quasi-Monte Carlo can achieve O(N−1). Several methods exist to increase its convergence to O(N−α ), α > 1, if the integrand has enough smoothness. We discuss two methods: lattice rules with periodization ...

In problems of moderate dimensions, the quasi-Monte Carlo method usually provides better estimates than the Monte Carlo method. However, as the dimension of the problem increases, the advantages of the quasi-Monte Carlo method diminish quickly. A remedy for this problem is to use hybrid sequences; sequences that combine pseudorandom and low-discrepancy vectors. In this paper we discuss a partic...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, which we proposed in an earlier paper [32], to the evaluation of an European Call option and of an Asian Call option. We assume that the stock price of the underlying asset S = S(t) is driven by a Lévy process Z(t), with independent increments distributed according to a NIG distribution. We compare our method with the ...

Quasi-random (or low discrepancy) sequences are sequences for which the convergence to the uniform distribution on [0; 1)s occurs rapidly. Such sequences are used in quasi-Monte Carlo methods for which the convergence speed, with respect to the N first terms of the sequence, is in O(N 1(lnN)s), where s is the mathematical dimension of the problem considered. The disadvantage of these methods is...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, developed by us in a previous paper [31], to the evaluation of barrier options. We assume that the stock price of the underlying asset is driven by a Lévy process with independent increments distributed according to a NIG distribution. We also provide numerical results that compare our method with the Monte Carlo metho...

So you're new to the idea of risk analysis, and you've got a lot of questions. What is risk? What do we mean by a "model?" What exactly is Monte Carlo simulation? Is anyone in your industry using this technique? This article is a simple overview to help you to understand what risk analysis is and why Monte Carlo simulation has become an increasingly popular and necessary technique for business ...

In an effort to avoid random-walk behaviour, many Markov Chain Monte Carlo methods use proposals based on dynamics related to the target distribution. The Hybrid Monte Carlo (HMC) is based on Hamiltonian dynamics and others the potential advantage of allowing global moves while retaining high probability acceptance. After reviewing the HMC method, I shall study strategies for the construction o...