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Value at risk (VaR) is a market risk measure widely used by risk managers and market regulatory authorities, and various methods are proposed in the literature for its estimation. However, limited studies discuss its distribution or its confidence intervals. The purpose of this paper is to compare different techniques for computing such intervals to identify the scenarios under which such confidence interval techniques perform properly.

The methods that are included in the comparison are based on asymptotic normality, extreme value theory and subsample bootstrap. The evaluation is done by computing the coverage rates for each method through Monte Carlo simulations under certain scenarios. The scenarios consider different persistence degrees in mean and variance, sample sizes, VaR probability levels, confidence levels of the intervals and distributions of the standardized errors. Additionally, an empirical application for the stock market index returns of G7 countries is presented.

The simulation exercises show that the methods that were considered in the study are only valid for high quantiles. In particular, in terms of coverage rates, there is a good performance for VaR(99 per cent) and bad performance for VaR(95 per cent) and VaR(90 per cent). The results are confirmed by an empirical application for the stock market index returns of G7 countries.

The findings of the study suggest that the methods that were considered to estimate VaR confidence interval are appropriated when considering high quantiles such as VaR(99 per cent). However, using these methods for smaller quantiles, such as VaR(95 per cent) and VaR(90 per cent), is not recommended.

This study is the first one, as far as it is known, to identify the scenarios under which the methods for estimating the VaR confidence intervals perform properly. The findings are supported by simulation and empirical exercises.

The singular perturbation character of the semiconductor device problem is well known by now. Various results on the structure of solutions (i.e. existence of spatial and temporal layers) have been obtained by means of singular perturbation theory. We use a rescaled form of the equations, which describes the evolution on the fast time scale, and discuss the asymptotic behavior of this system, i.e. its relationship to the initial layer problem, to the corresponding stationary problem and to the reduced problem. We show that the transient semiconductor problem fits in the framework of ‘fast reaction‐slow diffusion’ type equations, which are known from the analysis of chemical reacting systems. We use a multiple time scale expansion to give a new ‘dynamical’ derivation of the reduced problem.

We determine the effects of micro‐inertia density and the vortex viscosity on laminar free convection boundary layer flow of a thermomicropolar fluid past a vertical plate with exponentially varying surface temperature as well as surface heat flux. The governing nonsimilarity boundary layer equations are analyzed using: first, a series solution for small ξ (a scaled streamwise distribution of micro‐inertia density), second, an asymptotic solution for large ξ and, third, a full numerical solution implicit finite difference method together with Keller‐box scheme. Results are expressed in terms of local skin friction and local Nusselt number. The effects of varying the vortex viscosity parameter, Δ, surface temperature and the surface heat flux gradient n and m respectively against ξ for fluids having Prandtl number equals 0.72 and 7.0 are determined.

The purpose of this paper is the comparative analysis of Haar Wavelet Method and Optimal Homotopy Asymptotic Method for fractional Fisher type equation. In this paper, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), have been presented. The Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like the Fisher type. The approximate solutions of the fractional Fisher-type equation are compared with those of OHAM and with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than the Haar wavelet method.

Comparisons between the solutions obtained by the Haar wavelet method and OHAM with the exact solutions exhibit that both featured methods are effective and efficient in solving nonlinear problems.

The comparative results indicate that OHAM provides a more accurate value than the Haar wavelet method.

In this paper, two reliable techniques, the Haar wavelet method and OHAM, have been proposed for solving nonlinear fractional partial differential equation, i.e. fractional Fisher-type equation. The proposed novel methods are well suited for only nonlinear fractional partial differential equations. It also exhibits that the proposed method is a very efficient and powerful technique in finding the solutions for the nonlinear time fractional differential equations. The main significance of the proposed method is that it requires less amount of computational overhead in comparison to other numerical and analytical approximate methods. The application of the proposed methods for the solutions of time fractional Fisher-type equations satisfactorily justifies its simplicity and efficiency.

The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved.

The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases.

An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation.

The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

State of the art programs for the solution of the drift diffusion semiconductor equations are based on finite difference techniques, or on certain combinations of finite elements and finite differences. The extreme gradients which occur in semiconductor devices have motivated several attempts to exploit perturbation analysis in order to improve the numerical scheme. Selberherr, Markowich et. al. showed the singular perturbation nature of the drift diffusion equations. Their analytic approximations of diodes influenced some aspects of the Minimos and Bambi simulators. Asymptotic analyses of MOSFET were presented by Brews and by Ward. These solutions are mainly valid for long channels, and their accuracy is limited.

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension effect.

The method of matched asymptotic expansion is used to explore the rich dynamics near the exit where a stress singularity occurs. A boundary layer approach is also proposed to capture the flow further downstream where the free surface layer has grown significantly.

The jet is found to always contract near the tube exit. In contrast to existing numerical studies, the author explores the strength of upstream influence and the flow in the wall layer, resulting from jet contraction. This influence becomes particularly evident from the nonlinear pressure dependence on the upstream distance, as well as the pressure undershoot and overshoot at the exit for weak and strong gravity levels, respectively. The approach is validated against existing experimental and numerical data for the jet profile and centerline velocity where good agreement is obtained. Far from the exit, the author shows how the solution in the diffusive region can be matched to the inviscid far solution, providing the desired appropriate initial condition for the inviscid far flow solution. The location, at which the velocity becomes uniform across the jet, depends strongly on the gravity level and exhibits a non-monotonic behavior with respect to gravity and applied pressure gradient. The author finds that under weak gravity, surface tension has little influence on the final jet radius. The work is a crucial supplement to the existing numerical literature.

Given the presence of the stress singularity at the exit, the work constitutes a superior alternative to a computational approach where the singularity is typically and inaccurately smoothed over. In contrast, in the present study, the singularity is entirely circumvented. Moreover, the flow details are better elucidated, and the various scales involved in different regions are better identified.

In this paper, we consider the estimation of volatility parameters in the context of a linear regression where the disturbances follow a stochastic volatility (SV) model of order one with Gaussian log-volatility. The linear regression represents the conditional mean of the process and may have a fairly general form, including for example finite-order autoregressions. We provide a computationally simple two-step estimator available in closed form. Under general regularity conditions, we show that this two-step estimator is asymptotically normal. We study its statistical properties by simulation, compare it with alternative generalized method-of-moments (GMM) estimators, and present an application to the S&P composite index.

Efficient numerical assessment of performance is particularly important in digital material design of porous materials. This study aims to present an up-scaled approach to virtually investigate permeation of fluids through a real porous filter membrane with a heterogeneous micro-structure.

The method of asymptotic homogenization is applied. The structural parameters of the micro-structure are directly obtained from structural equation modeling image analysis of a commercial filter membrane without fitting procedures. The simulation results are compared to permeation experiments of gaseous nitrogen and liquid water.

The authors found that variations in the pressure gradients across the membrane, resulting from the heterogeneity of pore structure, need to be considered. Remarkable agreement between simulations and experiments is observed.

Despite some research in the field of filtration, no studies on filter membranes have been published yet, although they represent a large segment of filtration technology.

This paper is concerned with estimation and inference for difference-in-difference regressions with errors that exhibit high serial dependence, including near unit roots, unit roots, and linear trends. We propose a couple of solutions based on a parametric formulation of the error covariance. First stage estimates of autoregressive structures are obtained by using the Han, Phillips, and Sul (2011, 2013) X-differencing transformation. The X-differencing method is simple to implement and is unbiased in large N settings. Compared to similar parametric methods, the approach is computationally simple and requires fewer restrictions on the permissible parameter space of the error process. Simulations suggest that our methods perform well in the finite sample across a wide range of panel dimensions and dependence structures.