Uncertainty and energy-sector equity returns in Iran:a Bayesian and quasi-Monte Carlo time-varying analysis

This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically considers the refining,drilling,and petrochemical equity sectors of the Tehran Stock Exchange.The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model,and a complementary Bayesian network analysis is also conducted.The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty.This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models.Although these methods provide improvements by restricting the analysis to a specific price-regime period,they produce conflicting results,rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets.Nevertheless,the results indicate that the OPEC(historical)price volatility has a stronger effect on the energy sectors than the implied volatility has.These types of oil price shocks are found to have no effect on the drilling sector price pattern,whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks,respectively,gaining dominance in the oil market.

Quasi-Monte Carlo Simulation-Based SFEM for Slope Reliability Analysis

Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.

Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models

In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.

Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations

Deep learning has achieved great success in solving partial differential equations(PDEs),where the loss is often defined as an integral.The accuracy and efficiency of these algorithms depend greatly on the quadrature method.We propose to apply quasi-Monte Carlo(QMC)methods to the Deep Ritz Method(DRM)for solving the Neumann problems for the Poisson equation and the static Schr¨odinger equation.For error estimation,we decompose the error of using the deep learning algorithm to solve PDEs into the generalization error,the approximation error and the training error.We establish the upper bounds and prove that QMC-based DRM achieves an asymptotically smaller error bound than DRM.Numerical experiments show that the proposed method converges faster in all cases and the variances of the gradient estimators of randomized QMC-based DRM are much smaller than those of DRM,which illustrates the superiority of QMC in deep learning over MC.

Quasi-Monte Carlo simulation of Brownian sheet with application to option pricing

Monte Carlo and quasi-Monte Carlomethods arewidely used in scientific studies.As quasi-Monte Carlo simulations have advantage over ordinaryMonte Carlomethods,this paper proposes a new quasi-Monte Carlo method to simulate Brownian sheet via its Karhunen–Loéve expansion.The proposed new approach allocates quasi-random sequences for the simulation of random components of the Karhunen–Loéve expansion by maximum reducing its variability.We apply the quasi-MonteCarlo approach to an option pricing problem for a class of interest rate models whose instantaneous forward rate driven by a different stochastic shock through Brownian sheet andwe demonstrate the application with an empirical problem.

A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods

Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality.It is not evident which method is best,specially on random models of physical phenomena.We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media.In particular,we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal process.The suitability of each technique is identified in terms of computational cost and error tolerance.

Variance reduction for generalized likelihood ratio method by conditional Monte Carlo and randomized Quasi-Monte Carlo methods

The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.

Minimum Quadratic Distance Methods Using Grouped Data for Parametric Families of Copulas

Minimum quadratic distance (MQD) methods are used to construct chi-square test statistics for simple and composite hypothesis for parametric families of copulas. The methods aim at grouped data which form a contingency table but by defining a rule to group the data using Quasi-Monte Carlo numbers and two marginal empirical quantiles, the methods can be extended to handle complete data. The rule implicitly defines points on the nonnegative quadrant to form quadratic distances and the similarities of the rule with the use of random cells for classical minimum chi-square methods are indicated. The methods are relatively simple to implement and might be useful for applied works in various fields such as actuarial science.

Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects

Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.

Stochastic Economic Dispatch Considering the Dependence of Multiple Wind Farms Using Multivariate Gaussian Kernel Copula

Wind farms usually cluster in areas with abundant wind resources.Therefore,spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power penetration.This paper proposes a novel non-parametric copula method,multivariate Gaussian kernel copula(MGKC),to describe the dependence structure of wind speeds among multiple wind farms.Wind speed scenarios considering the dependence among different wind farms are sampled from the MGKC by the quasi-Monte Carlo(QMC)method,so as to solve the stochastic economic dispatch(SED)problem,for which an improved meanvariance(MV)model is established,which targets at minimizing the expectation and risk of fuel cost simultaneously.In this model,confidence interval is applied in the wind speed to obtain more practical dispatch solutions by excluding extreme scenarios,for which the quantile-copula is proposed to construct the confidence interval constraint.Simulation studies are carried out on a modified IEEE 30-bus power system with wind farms integrated in two areas,and the results prove the superiority of the MGKC in formulating the dependence among different wind farms and the superiority of the improved MV model based on quantilecopula in determining a better dispatch solution.

Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

Efficient numerical evaluation of Feynman integrals

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with O（10^（-3））accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multiloop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.

Using QMC Simulation for American-style Call Option Pricing

The development of the option price theory provides business enterprise a beneficial tool to carry through property risk management, but a variety of option price theories are established on certain environments, and they can not deal with crisis in uncertain environments precisely and quickly, especially when multi-factors change at the same time. Thus, price the option in uncertain environment has been becoming an important direction of research. In this paper, wc take the stock option for example~ using Quasi-Monte Carlo method to price the American-style option, and then provide an example to explain. The powerful assistant decision-making ability of the computer simulation is clearly expressed when we study and analyze the Quasi-Monte Carlo method＇s characteristics.

ON THE CONVERGENCE OF SEQUENTIAL NUMBER-THEORETIC METHOD FOR OPTIMIZATION

In the present note the convergence problem of the sequential number-theoretic method for optimization proposed by Fang and Wang is studied, the convergence criteria and the estimation of errors concerning this algorithm are given.