Dirichlet级数和随机Dirichlet级数的下级增长性

本文研究了全平面上零级和有限级Dirichlet级数及随机Dirichlet级数的下级增长性.利用型函数,得到了其系数和增长性之间的关系,以及当随机变量序列{X_n(ω)}满足一定条件时,零级和有限级随机Dirichlet级数在全平面上所确定的随机整函数在每条水平直线上的下级增长性几乎必然与相应的随机Dirichlet级数的下级增长性相同.     

基于统一价格拍卖的初始排污权分配方法

针对初始排污权总量分配的实际问题,基于统一价格拍卖的思想提出了一种具有激励性的可变总量的分配方法,分别给出了排污企业对称和排污企业非对称两种情形下的线性均衡报价策略,并证明了该方法的可行性和有效性,从而为建设排污权分配和交易制度提供了理论依据和方法参考.     

Saddle-point solutions to Dirichlet problems on the Sierpiński gasket

We provide sufficient conditions for the existence of saddle-point solutions to a system driven by the weak Laplacian on the Sierpiński gasket. We analyze also its stability by proving its continuous dependence on parameters.     

An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cramér–Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model.     

Conditional tail risk measures for the skewed generalised hyperbolic family

This paper deals with the estimation of loss severity distributions arising from historical data on univariate and multivariate losses. We present an innovative theoretical framework where a closed-form expression for the tail conditional expectation (TCE) is derived for the skewed generalised hyperbolic (GH) family of distributions. The skewed GH family is especially suitable for equity losses because it allows to capture the asymmetry in the distribution of losses that tends to have a heavy right tail. As opposed to the widely used Value-at-Risk, TCE is a coherent risk measure, which takes into account the expected loss in the tail of the distribution. Our theoretical TCE results are verified for different distributions from the skewed GH family including its special cases: Student-t, variance gamma, normal inverse gaussian and hyperbolic distributions. The GH family and its special cases turn out to provide excellent fit to univariate and multivariate data on equity losses. The TCE risk measure computed for the skewed family of GH distributions provides a conservative estimator of risk, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from the loss distribution. We extend our analysis to the multivariate framework when modelling portfolios of losses, allowing the multivariate GH distribution to capture the combination of correlated risks and demonstrate how the TCE of the portfolio can be decomposed into individual components, representing individual risks in the aggregate (portfolio) loss.     

A hybrid descent method for solving a convex constrained optimization problem with applications

The purpose of this paper is to introduce a hybrid descent algorithm for finding a common point in fixed‐point sets of quasi‐nonexpansive mappings and solution sets of variational inequality problems. In the framework of Hilbert spaces, the strong convergence of the hybrid descent algorithm is established. Numerical experiments for the bandwidth allocation, which demonstrate the effectiveness, performance, and convergence of the proposed algorithm, are provided.     

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.     

Balanced allocation on graphs: A random walk approach

We propose algorithms for allocating n sequential balls into n bins that are interconnected as a d‐regular n‐vertex graph G, where d ≥ 3 can be any integer. In general, the algorithms proceeds in n succeeding rounds. Let ? > 0 be an integer, which is given as an input to the algorithms. In each round, ball 1 ≤ t ≤ n picks a node of G uniformly at random and performs a nonbacktracking random walk of length ? from the chosen node and simultaneously collects the load information of a subset of the visited nodes. It then allocates itself to one of them with the minimum load (ties are broken uniformly at random). For graphs with sufficiently large girths, we obtain upper and lower bounds for the maximum number of balls at any bin after allocating all n balls in terms of ?, with high probability.     

The Latent Scale Covariogram: A Tool for Exploring the Spatial Dependence Structure of Nonnormal Responses

When modeling spatially distributed normal responses Y_i in terms of vectors x_i of explanatory variables, one may fit a linear model assuming independence, and then use the empirical variogram of the residuals to determine an appropriate parametric form for the autocorrelation function. Suppose, however, that the responses are not normally distributed—for example, Poisson or Bernoulli. One may model spatial dependence using a hierarchical generalized linear model in which, conditional on a latent Gaussian field Z = {Z_i}, the Y_i have independent distributions from the exponential family, with an appropriate link function connecting their conditional means with the linear predictors x^t_iβ + Z_i. The question then is how to determine an appropriate model for the autocorrelation function of Z. The empirical variogram of the Y_i is no longer appropriate, since (unless the link function is the identity) it is on the wrong scale. We propose here an alternative, the latent scale covariogram, whose graph reflects the autocorrelation structure of the underlying normal field. We illustrate its use on several real datasets, together with a simulated dataset, and obtain results quite different from those obtained using the variogram. Supplementary materials for this article are available online.     

Several Expressions of Dirichlet L-function at Positive Integers

In this paper, by making use of Abel's theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.