Exponential Stability for Time-changed Stochastic Differential Equations

Acta Mathematicae Applicatae Sinica, English Series - So far there have been few results presented on the exponential stability for time-changed stochastic differential equations. The main aim of...     

Novel biogeography-based optimization algorithm with hybrid migration and global-best Gaussian mutation

The Biogeography-Based Optimization algorithm and its variants have been used widely for optimization problems. To get better performance, a novel Biogeography-Based Optimization algorithm with Hybrid migration and global-best Gaussian mutation is proposed in this paper. Firstly, a linearly dynamic random heuristic crossover strategy and an exponentially dynamic random differential mutation one are presented to form a hybrid migration operator, and the former is used to get stronger local search ability and the latter strengthen the global search ability. Secondly, a new global-best Gaussian mutation operator is put forward to balance exploration and exploitation better. Finally, a random opposition learning strategy is merged to avoid getting stuck in local optima. The experiments on the classical benchmark functions and the complexity functions from CEC-2013 and CEC-2017 test sets, and the Wilcoxon, Bonferroni-Holm and Friedman statistical tests are used to evaluate our algorithm. The results show that our algorithm obtains better performance and faster running speed compared with quite a few state-of-the-art competitive algorithms. In addition, experimental results on Minimum Spanning Tree and K-means clustering optimization show that our algorithm can cope with these two problems better than the comparison algorithms.     

Projection-based Consistent Test for Linear Regression Model with Missing Response and Covariates

Acta Mathematicae Applicatae Sinica, English Series - In recent years, there has been a large amount of literature on missing data. Most of them focus on situations where there is only missingness...     

Characterization of acceptance sets for co-monotone risk measures

We present a geometric characterization of acceptance sets for monotone, co-monotone and convex risk measures on finite state spaces. Geometrically, such acceptance sets can be represented by convex polygons with edges only on certain hyperplanes. We also provide some lower dimensional examples, and study acceptance sets for value at risk and expected shortfall.     

Haezendonck–Goovaerts risk measure with a heavy tailed loss

Recently Haezendonck–Goovaerts (H–G) risk measure has received much attention in (re)insurance and portfolio management. Some nonparametric inferences have been proposed in the literature. When the loss variable does not have enough moments, which depends on the involved Young function, the nonparametric estimator in Ahn and Shyamalkumar (2014) has a nonnormal limit, which challenges interval estimation. Motivated by the fact that many loss variables in insurance and finance could have a heavier tail such as an infinite variance, this paper proposes a new estimator which estimates the tail by extreme value theory and the middle part nonparametrically. It turns out that the proposed new estimator always has a normal limit regardless of the tail heaviness of the loss variable. Hence an interval with asymptotically correct confidence level can be obtained easily either by the normal approximation method via estimating the asymptotic variance or by a bootstrap method. A simulation study and real data analysis confirm the effectiveness of the proposed new inference procedure for estimating the H–G risk measure.     

Pareto-optimal reinsurance arrangements under general model settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.     

M-矩阵线性互补问题模系多分裂迭代方法的收敛性

首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理.     

Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Assume that a quadratic matrix-valued function \(\psi (X) = Q - X^{\prime }PX\) is given and let \(\mathcal{S} = \left\{ X\in {\mathbb R}^{n \times m} \, | \, \mathrm{trace}[\,(AX - B)^{\prime }(AX - B)\,] = \min \right\} \) be the set of all least-squares solutions of the linear matrix equation \(AX = B\). In this paper, we first establish explicit formulas for calculating the maximum and minimum ranks and inertias of \(\psi (X)\) subject to \(X \in {\mathcal S}\), and then derive from the formulas the analytic solutions of the two optimization problems \(\psi (X) =\max \) and \(\psi (X)= \min \) subject to \(X \in \mathcal{S}\) in the Löwner partial ordering. As applications, we present a variety of results on equalities and inequalities of the ordinary least squares estimators of unknown parameter vectors in general linear models.     

A DFT study of formaldehyde adsorption on functionalized graphene nanoribbons

Density functional theory (DFT) based ab initio calculations were done to monitor the formaldehyde (CHOH) adsorptive behavior on pristine and Ni-decorated graphene sheet. Structural optimization indicates that the formaldehyde molecule is physisorbed on the pristine sheet via partly weak van der Waals attraction having the adsorption energy of about −15.7 kcal/mol. Metal decorated sheet is able to interact with the CHOH molecule, so that single Ni atoms prefer to bind strongly at the bridge site of graphene and each metal atom bound on sheet may adsorb up to four CHOH. The findings also show that the Ni decoration on graphene surface results in some changes in electronic properties of the sheet and its E_g is remained unchanged after adsorption of CHOH molecules. It is noteworthy to say that no bond cleavage was observed for the adsorption of CHOH on Ni-decorated graphene.