Optimal joint survival reinsurance: An efficient frontier approach

The problem of optimal excess of loss reinsurance with a limiting and a retention level is considered. It is demonstrated that this problem can be solved, combining specific risk and performance measures, under some relatively general assumptions for the risk model, under which the premium income is modelled by any non-negative, non-decreasing function, claim arrivals follow a Poisson process and claim amounts are modelled by any continuous joint distribution. As a performance measure, we define the expected profits at time x of the direct insurer and the reinsurer, given their joint survival up to x, and derive explicit expressions for their numerical evaluation. The probability of joint survival of the direct insurer and the reinsurer up to the finite time horizon x is employed as a risk measure. An efficient frontier type approach to setting the limiting and the retention levels, based on the probability of joint survival considered as a risk measure and on the expected profit given joint survival, considered as a performance measure is introduced. Several optimality problems are defined and their solutions are illustrated numerically on several examples of appropriate claim amount distributions, both for the case of dependent and independent claim severities.     

Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model

In this paper, we study numerical approximations of a nonlinear eigenvalue problem and consider applications to a density functional model. We prove the convergence of numerical approximations. In particular, we establish several upper bounds of approximation errors and report some numerical results of finite element electronic structure calculations that support our theory. Copyright © 2010 John Wiley & Sons, Ltd.     

基于极大模理想点法的投资组合决策模型分析

基于马克维茨投资组合模型的均值一方差理论,构建一种投资组合收益和风险在一定范围的双目标线性模糊优化模型,并尝试采用极大模理想点法来求解该模型．最后,给出一实际算例,对一具体投资组合模型进行研究,结果表明：本文所采用的极大模理想点法是可行的、有效的;本文所采用的算法比已有文献给出的模糊线性规划法具有更加广泛意义的优化结果．     

全时段最优套期保值模型及实证研

针对传统套期保值模型只考虑套期保值资产在套期保值期末的风险及未能充分利用样本数据所提供的信息的问题,本文提出了一类同时考虑套期保值期内不同期限风险的全时段最优套期保值比率计算模型.全时段套期保值模型通过最小化套期保值资产在套期保值期内不同期限的风险将投资者面临的风险在整个套期保值期内稳定保持在一个较低的水平,并更充分的利用了资产历史价格样本数据所提供的信息.本文基于沪深300指数及其仿真股指期货的历史价格数据,对传统形式的三种套期保值模型与本文提出的三种全时段套期保值模型的套期保值效果进行了实证分析和比较,并使用GARCH模型比较分析了这些模型套期保值的动态效果,结果表明三种全时段模型的套期保值效果都要优于相应的传统模型,能有效地缓解提前终止套期保值时投资者所面临的风险.     

Portfolio selection in stochastic markets with HARA utility functions

In this paper, we consider the optimal portfolio selection problem where the investor maximizes the expected utility of the terminal wealth. The utility function belongs to the HARA family which includes exponential, logarithmic, and power utility functions. The main feature of the model is that returns of the risky assets and the utility function all depend on an external process that represents the stochastic market. The states of the market describe the prevailing economic, financial, social, political and other conditions that affect the deterministic and probabilistic parameters of the model. We suppose that the random changes in the market states are depicted by a Markov chain. Dynamic programming is used to obtain an explicit characterization of the optimal policy. In particular, it is shown that optimal portfolios satisfy the separation property and the composition of the risky portfolio does not depend on the wealth of the investor. We also provide an explicit construction of the optimal wealth process and use it to determine various quantities of interest. The return-risk frontiers of the terminal wealth are shown to have linear forms. Special cases are discussed together with numerical illustrations.     

UNO DMRG CAS CI calculations of binuclear manganese complex Mn(IV)2O2(NHCHCO2)4: Scope and applicability of Heisenberg model

Both direct exchange and super-exchange interactions cooperate to realize inter-spin magnetic interaction in binuclear manganese complex Mn(IV)₂O₂(NHCHCO₂)₄ with a di-μ-oxo path. We revisited this spin system using DMRG CAS methods and CAS selection procedures. Our results indicate that our previous “dynamically extended spin polarization” (DE-SP) procedure for organic polyradicals and so forth does not work well. Thus, we have examined another selection procedure, the “dynamically extended super-exchange” (DE-SE) procedure. DMRG CASCI [18,18] by UB3LYP(HS)-UNO(DE-SE) can realize antiferromagnetic J values similar to experimental ones (−87 cm⁻¹). In addition, all J values between all spin states (HS[septet],IS[quintet],IS[triplet],LS[singlet])were also shown to be correct under sufficiently large M values. © 2018 Wiley Periodicals, Inc.     

平板式螺旋相位板的设计与应用

传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件,由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数.本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板.通过理论分析与数值模拟,发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束,而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节.为了实际应用的需要,可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束.这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.     

First-principles calculation of temperature-dependent electronic transitions mechanism in V or Nb substituted BiFeO3

Here, we present a simulation study of temperature-dependent electronic transitions in BiVO₃ (BVO) and BiNbO₃ (BNO) using density functional theory (DFT) together with generalized gradient approximation (GGA) and two-dimensional correlation analysis (2D-CA). The results indicate that heat accumulation can accelerate the degeneracy of V-3d orbital in BVO and the splitting of Nb-4d orbital in BNO at 750 K. We found changes in the type of d–p hybrid orbital as follows, for BVO: V-d_x²_+y² + d_Z²-O-2p_z → V-d_x²_+y²-O-2p_z; and for BNO: Nb-d_x²_+y²-O-2p_z → Nb-d_x²_+y² + d_Z²-O-2p_z. Furthermore, we found changes in the type of hybrid orbital leading to the following electron–electron interactions, for BVO: t_2g (V-d_Z²-O-2p_z) + e_g (V-d_x²_+y²-O-2p_z) → t_2g (V-d_x²_+y²-O-2p_z); and for BNO: t_2g + e_g (Nb-d_x²_+y² + d_Z²-O-2p_z) → t_2g (Nb-d_x²_+y²-O-2p_z) + e_g (Nb-d_z²-O-2p_z). The electronic transitions are determined by a charge-transfer from the occupied O-2p⁴ orbitals to the unoccupied V-3d³ (or Nb-4d³) and Bi-6p³ orbitals. Due to the temperature-dependent electronic structure closely related to these electronic transitions, this study provides a new perspective for the design and improvement of BFO-based temperature-sensitive devices.     

汉克-贝塞尔光束在海洋湍流信道中的螺旋相位谱分析

携带轨道角动量的汉克-贝塞尔(Hankel-Bessel,HB)光束具有无衍射和自聚焦特性,用来作为信息传输的载体有望增大信息传输容量.基于Rytov近似理论,推导得到了HB涡旋光束经过海洋水平弱湍流信道后的螺旋相位谱的解析表达式,并利用数值仿真方法研究了海洋湍流参数对轨道角动量模式探测概率的影响.结果表明,海洋湍流导致发射轨道角动量模式的探测概率下降,出现模式串扰和螺旋相位谱扩展.海洋湍流对HB涡旋光束的负面影响随着轨道角动量模式数、传输距离、温度方差耗散率的增加而增强,随湍流动能耗散率的增加而减弱.HB涡旋光束受以盐度波动驱动的海洋湍流的负面影响更大.另外,在弱湍流及几十米传输距离条件下,HB涡旋光束的传输性能要差于最佳束腰大小设置的拉盖尔-高斯涡旋光束.这些结果有望为海洋环境水下光通信链路的实现提供一定的参考价值.     

阿比特龙的红外光谱与前线轨道

采用密度泛函理论的B3LYP混合泛函和6-311G(d,p)基组,通过几何结构优化得到了阿比特龙分子的稳定构型.计算了阿比特龙分子的红外吸收光谱,并与文献数据进行比较,将2971.01、1588.31、1536.13、1450.40、1112.13和1074.44 cm~(-1)等处吸收峰指认为特征吸收峰.在优化计算的基础上,结合Multiwfn软件分析了阿比特龙分子的前线轨道成分,得出阿比特龙分子的亲核能力明显强于其亲电能力,C55、O54原子在95αHOMO中占据的权重分别为61.79%和17.05%,C=O-H部位是其亲核反应的活性中心.研究结果对阿比特龙分子的检测、活性应用等方面具有一定的理论指导意义.