Other than common random numbers, control varlates is the most promising variance reduction technique in terms of its potential for widespread use: Control variates is applicable in single or multiple response simulation, it does not require altering the simulation run in any way, and any stochastic simulation contains potential control variates. A rich theory of control variates has been devel...

Model sensitivity analysis variance reduction ( ) ( ), where ( ) ∑ ( )[ ( )] , ( ) ∑ ( )[ ( )] , ( ) ∑ ( ) , where is the numeric real value of state q, ( ) is the expected real value of Q before applying new findings, ( ) is the expected real value of Q after applying new findings f for variable F, and ( ) is the variance of the real value of Q before any new findings [0,infinity], the greater...

This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (1995) for an iterative sampling-based decomposition algorithm, introduced by Dantzig and Glynn (1990) and Infanger (1992), for solving two-stage stochastic programs. Extensions of the theory to cover use of variance reduction, different iterative sampling s...

Dimensionality reduction procedures such as principal component analysis and the maximum margin criterion discriminant are special cases of a weighted maximum variance (WMV) approach. We present a simple two parameter version of WMV that we call 2P-WMV. We study the classification error given by the 1-nearest neighbor algorithm on features extracted by our and other dimensionality reduction met...

All the results of the preceding lecture show that the ratio σ/ √ N governs the accuracy of a Monte-Carlo method with N simulations. An obvious consequence of this fact is that one always has interest to rewrite the quantity to compute as the expectation of a random variable which has a smaller variance : this is the basic idea of variance reduction techniques. For complements, we refer the rea...

\Knowledge of either analytical or numerical approximations should enable more eecient simulation estima-tors to be constructed." This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. We present a new approach for Markov processes that relies on the construction of a martingale that is strongly c...

We propose a new estimator of steady-state blocking probabilities for simulations of stochastic loss models that can be much more e cient than the natural estimator (ratio of losses to arrivals). The proposed estimator is a convex combination of the natural estimator and an indirect estimator based on the average number of customers in service, obtained from Little's law (L = W ), which exploit...

This paper presents an overview of techniques for improving the efficiency of option pricing simulations, including quasiMonte Carlo methods, variance reduction, and methods for dealing with discretization error.

We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep h has a variance which is O(h−1/2) for discontinuous payoffs and O(1) for continuous ...

Stochastic particle methods for the coagulation-fragmentation Smoluchowski equation are developed and a general variance reduction technique is suggested. This method generalizes the massow approach due to H. Babovsky, and has in focus the desired band of the size spectrum. Estimations of the variance and bias of the method are derived. A comparative cost and variance analysis is made for the k...