Results 1  10
of
19
A randomized quasiMonte Carlo simulation method for Markov chains
 Operations Research
, 2007
"... Abstract. We introduce and study a randomized quasiMonte Carlo method for estimating the state distribution at each step of a Markov chain. The number of steps in the chain can be random and unbounded. The method simulates n copies of the chain in parallel, using a (d + 1)dimensional highlyunifor ..."
Abstract

Cited by 27 (9 self)
 Add to MetaCart
(Show Context)
Abstract. We introduce and study a randomized quasiMonte Carlo method for estimating the state distribution at each step of a Markov chain. The number of steps in the chain can be random and unbounded. The method simulates n copies of the chain in parallel, using a (d + 1)dimensional highlyuniform point set of cardinality n, randomized independently at each step, where d is the number of uniform random numbers required at each transition of the Markov chain. This technique is effective in particular to obtain a lowvariance unbiased estimator of the expected total cost up to some random stopping time, when statedependent costs are paid at each step. It is generally more effective when the state space has a natural order related to the cost function. We provide numerical illustrations where the variance reduction with respect to standard Monte Carlo is substantial. The variance can be reduced by factors of several thousands in some cases. We prove bounds on the convergence rate of the worstcase error and variance for special situations. In line with what is typically observed in randomized quasiMonte Carlo contexts, our empirical results indicate much better convergence than what these bounds guarantee.
Strictly Deterministic Sampling Methods in Computer Graphics
 SIGGRAPH 2003 Course Notes, Course #44: Monte Carlo Ray Tracing
, 2003
"... We introduce a strictly deterministic, meaning nonrandom, rendering method, which performs superior to state of the art Monte Carlo techniques. Its simple and elegant implementation on parallel computer architectures is capable of simulating antialiasing, motion blur, depth of field, area light so ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
We introduce a strictly deterministic, meaning nonrandom, rendering method, which performs superior to state of the art Monte Carlo techniques. Its simple and elegant implementation on parallel computer architectures is capable of simulating antialiasing, motion blur, depth of field, area light sources, glossy reflection and transmission, participating media, and global illumination. We provide a selfcontained exposition of the underlying mathematical principles and illustrate how the design of quasiMonte Carlo algorithms, i.e. strictly deterministic sampling methods based on number theory, is related to Monte Carlo algorithms based on probability theory.
Path Generation for QuasiMonte Carlo Simulation of Mortgage Backed Securities
 Management Science
, 2000
"... Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods, however in high d ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods, however in high dimensional problems special methods are required to ensure that the faster convergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown highdimensional examples, in which low discrepancy methods perform worse than Monte Carlo methods. The principal component construction introduced by Acworth et al. (1998) provides one solution to this problem. However, the computational effort required to generate each path grows quadratically with the dimension of the problem. This article presents two new methods that offer accuracy equivalent, in terms of explained variability, to the principal components construction with computational requirements that are linearly related to the probl...
On the Use of QuasiMonte Carlo Methods in Computational Finance
 Computational Science – ICCS 2001, Lecture Notes in Computer Science
"... . We give the background and required tools for applying ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
. We give the background and required tools for applying
FAST SIMULATION OF EQUITYLINKED LIFE INSURANCE CONTRACTS WITH A SURRENDER OPTION
"... In this paper, we consider equitylinked life insurance contracts that give their holder the possibility to surrender their policy before maturity. Such contracts can be valued using simulation methods proposed for the pricing of American options, but the mortality risk must also be taken into acc ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
In this paper, we consider equitylinked life insurance contracts that give their holder the possibility to surrender their policy before maturity. Such contracts can be valued using simulation methods proposed for the pricing of American options, but the mortality risk must also be taken into account when pricing such contracts. Here, we use the leastsquares Monte Carlo approach of Longstaff and Schwartz coupled with quasiMonte Carlo sampling and a control variate in order to construct efficient estimators for the value of such contracts. We also show how to incorporate the mortality risk into these pricing algorithms without explicitly simulating it. 1
Inverting the symmetrical beta distribution
 ACM TRANS. MATH. SOFTWARE. FORTHCOMING
, 2004
"... We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function and its inverse is found via Newton’s method. This algorithm can be used to generate beta random variates by in ..."
Abstract
 Add to MetaCart
We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function and its inverse is found via Newton’s method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.
200708 “Designing a Social Security Pension System”, Robert L. Brown
"... 200804 “An Accelerating QuasiMonte Carlo Method for Option Pricing Under the Generalized Hyperbolic Lévy ..."
Abstract
 Add to MetaCart
(Show Context)
200804 “An Accelerating QuasiMonte Carlo Method for Option Pricing Under the Generalized Hyperbolic Lévy