Monte Carlo Algorithms for the Extracting of Electrical Capacitance

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

The Performance of Some Restricted Estimators In Restricted Linear Regression Model

In the linear regression model, the restricted biased estimation as one of important methods to addressing the high variance and the multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison among them. According to the simulation study we observe that, the performance of the restricted modified unbiased ridge regression estimator (RMUR) was proposed by Bader and Alheety (2020) is better than of these estimators. Numerical example have been considered to illustrate the performance of the estimators.

A new modified ridge-type estimator for the beta regression model: simulation and application

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

Implementing de-biased estimators using mixed sequences

We describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.

Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options

We present the Forest of Stochastic Trees (FOST) method for pricing multiple exercise options by simulation. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options, hence extending that method to allow for a multi-dimensional underlying process. The FOST can also be viewed as extending the stochastic tree method for valuing (single exercise) American-style options to multiple exercise options. The proposed valuation method results in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. This method is of particular use in cases where there is potentially a large number of assets underlying the contract and/or the underlying price process depends on multiple risk factors. Numerical results are presented to illustrate the method.