Optimal dividend-equity issuance strategy in a dual model with fixed and proportional transaction costs

In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company’s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems: one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company’s reserve above zero by issuing new equity, depending on the model’s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.     

Correcting for biases in affected sib-pair linkage analysis caused by uncertainty in sibling relationship

When there is uncertainty in sibling relationship,the classical affected sib-pair(ASP) linkage tests may be severely biased.This can happen,for example,if some of the half sib-pairs are mixed with full sib-pairs.The genomic control method has been used in association analysis to adjust for population structures.We show that the same idea can be applied to ASP linkage analysis with uncertainty in sibling relationship.Assuming that,in addition to the candidate marker,null markers that are unlinked to the disease locus are also genotyped,we may use the information on these loci to estimate the proportion of half sib-pairs and to correct for the bias and variance distortion caused by the heterogeneity of sibling relationship.Unlike in association studies,the null loci are not required to be matched with the candidate marker in allele frequency for ASP linkage analysis.This makes our approach flexible in selecting null markers.In our simulations,using a number of 30 or more null loci can effectively remove the bias and variance distortion.It is also shown that,even the null loci are weakly linked to the disease locus,the proposed method can also provide satisfactory correction.     

WEIGHTED LASSO ESTIMATES FOR SPARSE LOGISTIC REGRESSION:NON-ASYMPTOTIC PROPERTIES WITH MEASUREMENT ERRORS

For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data.We propose two types of weighted Lasso estimates,depending upon covariates determined by the Mc Diarmid inequality.Given sample size n and a dimension of covariates p,the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the?1-estimation error and the squared prediction error of the unknown parameters.We compare the performance of our method with that of former weighted estimates on simulated data,then apply it to do real data analysis.     

STATIONARY SOLUTIONS OF THE RELATIVISTIC VLASOV-MAXWELL SYSTEM OF PLASMA PHYSICS

The authors consider the stationary relativistic coupled system consisting of Vlasov’s equation for the distribution function of charged particles and Maxwell''s equations for the electric and magnetic fields of a plasma. With different tools of nonlinear functional analysis the existence of solutions is proved, in which, according to different geometries and symmetries, the distribution function depends on one, two or three independent integrals of the motion.     

FINITE ELEMENT AND DISCONTINUOUS GALERKIN METHOD FOR STOCHASTIC HELMHOLTZ EQUATION IN TWO- AND THREE-DIMENSIONS

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.     

BIFURCATION OF SINGULAR POINTS NEAR A DOUBLE FOLD POINT INZ_2 -SYMMETRIC NONLINEAR EQUATIONS

We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.     

Distance-covariance-based tests for heteroscedasticity in nonlinear regressions

We use distance covariance to introduce novel consistent tests of heteroscedasticity for nonlinear regression models in multidimensional spaces. The proposed tests require no user-defined regularization, which are simple to implement based on only pairwise distances between points in the sample and are applicable even if we have non-normal errors and many covariates in the regression model. We establish the asymptotic distributions of the proposed test statistics under the null and alternative hypotheses and a sequence of local alternatives converging to the null at the fastest possible parametric rate. In particular, we focus on whether and how the estimation of the finite-dimensional unknown parameter vector in regression functions will affect the distribution theory. It turns out that the asymptotic null distributions of the suggested test statistics depend on the data generating process, and then a bootstrap scheme and its validity are considered. Simulation studies demonstrate the versatility of our tests in comparison with the score test, the Cramér-von Mises test,the Kolmogorov-Smirnov test and the Zheng-type test. We also use the ultrasonic reference block data set from National Institute of Standards and Technology of USA to illustrate the practicability of our proposals.     

A class of weighted estimators for additive hazards model in case-cohort studies

Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose＇a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.     

Recovering Unbounded Rough Surfaces with a Direct Imaging Method

In this paper,we consider the inverse acoustic scattering problem by an unbounded rough surface.A direct imaging method is proposed to reconstruct the rough surfaces from scattered-field data for incident plane waves and the performance analysis is also presented.The reconstruction method is very robust to noises of measured data and does’t need to know the type of the boundary conditions of the surfaces in advance.Finally,numerical examples are carried out to illustrate that our method is fast,accurate and stable even for the case of multiple-scale profiles.     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

VARIATIONAL DISCRETIZATION OF A CONTROL-CONSTRAINED PARABOLIC BANG-BANG OPTIMAL CONTROL PROBLEM

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.     

Robust Variable Selection and Estimation in Threshold Regression Model

We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model.It estimates regression coefficients as well as the threshold parameter robustly that can be resistant to outliers or heavy-tailed noises and perform variable selection simultaneously.We illustrate our approach with the absolute loss,the Huber’s loss,and the Tukey’s loss,it can also be extended to any other robust losses.Simulation studies are conducted to demonstrate the usefulness of our robust approach.Finally,we use our estimators to investigate the presence of a shift in the effect of debt on future GDP growth.     

A Semiparametric Additive-multiplicative Rates Model for the Weighted Composite Endpoint of Recurrent and Terminal Events

Recurrent event data are commonly encountered in many scientific fields, including biomedical studies, clinical trials and epidemiological surveys, and many statistical methods have been proposed for their analysis. In this paper, we consider to use a weighted composite endpoint of recurrent and terminal events, which is weighted by the severity of each event, to assess the overall effects of covariates on the two types of events. A flexible additive-multiplicative model incorporating both multi...     

On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.     

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.     

On multifractal of Cantor dust

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.     

Empirical likelihood-based inferences for the area under the ROC curve with covariates

In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test.Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy.In this paper,empirical likelihood (EL) method is proposed for the AUC regression model.For the regression parameter vector,it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions.Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem,as well as for the covariate-specific AUC.Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression.Finally,the proposed methods are illustrated with a real data set.     

Partition of Unity for a Class of Nonlinear Parabolic Equation on Overlapping Non-Matching Grids

A class of nonlinear parabolic equation on a polygonal domain Ω  R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.     

A COLLOCATION METHOD FOR THE CONDUCTIVITY PROBLEM WITH DISCONTINUOUS COEFFICIENT

In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.