Markov chain Monte Carlo (MCMC) methods have an important role in solving high dimensionality stochastic problems characterized by computational complexity. Given their critical importance, there is need for network and security risk management research to relate the MCMC quantitative...

In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes...

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency,...

The four most readily available tests of autocorrelation in dynamic models namely Durbin's M test, Durbin's H test, Breusch - Godfrey (BGF) test and Ljung and Box (Q) test are compared in terms of their power for varying sample sizes, levels of autocorrelation and significance using Monte Carlo...

We study an expansion of the cumulative distribution function of the standard normal random variable that results in a family of closed form approximations that converge at 0. One member of the family that has only five explicit constants offers the absolute error of 5.79 10^{-6} across the...

Investors typically measure an asset’s potential to diversify a portfolio by its correlations with the portfolio’s other assets, but correlation is useful only if it provides a good estimate of how an asset’s returns co-occur cumulatively with the other asset returns over the investor’s...

Introducing the Brownian motion in the way of Einstein and Wiener we find the connection between a Wiener Process and the Heat Diffusion PDE.We solve the PDE analytically for some boundary conditions and then use the connection to the Wiener Process to solve more complex BVP's using Monte Carlo...

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including multi-dimensional systems with stable eigenvalues...

This article demonstrates the use of two approaches to parallelizing a Garch(1,1) calibration algorithm. The base serial implementation is a genetic algorithm that uses maximum likelihood in the fitness function. This is written in generic C. The first type of parallelization involves...

We compare three alternative Maximum Likelihood Multidimensional Scaling methods for pairwise dissimilarity ratings, namely MULTISCALE, MAXSCAL, and gurations very well. The recovery of the true dimensionality depends on the test criterion (likelihood ratio test, AIC, or CAIC), as well as on the...