Safety first portfolio choice based on financial and sustainability returns

The aim of this paper is to expand the methodological spectrum of socially responsible investing by introducing stochastic sustainability returns into safety first models for portfolio choice. We provide a foundation of the notion of sustainability in portfolio theory and establish a general model for generalized safety first portfolio management with probabilistic constraints and three specifications of it. Moreover, we prove theorems about conditions for unique optimal solutions and for the constraints of one model being more restrictive than those of another. In an empirical part, we calculate the costs of investing according to our approach in terms of less financial return.     

Truth-telling and Nash equilibria in minimum cost spanning tree models

In this paper we consider the minimum cost spanning tree model. We assume that a central planner aims at implementing a minimum cost spanning tree not knowing the true link costs. The central planner sets up a game where agents announce link costs, a tree is chosen and costs are allocated according to the rules of the game. We characterize ways of allocating costs such that true announcements constitute Nash equilibria both in case of full and incomplete information. In particular, we find that the Shapley rule based on the irreducible cost matrix is consistent with truthful announcements while a series of other well-known rules (such as the Bird-rule, Serial Equal Split, and the Proportional rule) are not.     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

含有一阶导数的四阶边值问题正解的存在性

研究了含有一阶导数的四阶边值问题,利用度理论构造出的一个新的不动点定理,由Green函数的性质,给出了一类含有导数的四阶边值问题正解存在的充分条件,得到了边值问题正解存在的一些新结果.     

非线性分数微分方程边值问题正解的存在性(英文)

In this paper,we study a Dirichlet-type boundary value problem（BVP） of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D^α_o⁺is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.     

变系数非线性递归序列的极限

对形如F_(n+p)=(sum from to i=1 to p)a_i(n)F_(n+i-1)~(b_i),n≥1的变系数非线性递归序列{F_n}的极限问题进行了研究,给出了在满足一定条件时,序列{F_n}收敛且极限值与初始值F_i>0,i=1,2,…,p无关.     

应用复合极值理论计算VaR1

本文介绍了一种复合极值理论,并将其应用到VaR的计算上。实际中大的损失发生的频率也是风险的一种度量,在应用复合极值理论方法计算VaR时,我们第一次将在一定时期内金融资产的损失率超过一定阈值的次数的分布和收益率的分布结合了起来,对欧元/人民币、日元/人民币两种汇率进行了VaR的计算,经过实证分析,得到了一些有意义的结果。     

饮料罐尺寸的最优解证明及其优化设计

为了发掘节省原料的潜力,对销量很大的饮料易拉罐进行优化设计.建立起具有通用性的优化模型;运用压缩变量技术,解决了模型复杂不易求解的困难;给出了便于实施计算的一整套显式求解公式.通过方向导数分析和流动极值分析,证明了解的最优性,指出了目标函数的退化特征及其临界状态;结合数学理论分析、具体数值计算和实际工艺条件,形成了层层递进式的优化设计途径.     

Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation (?p^′(u^′))+q(t)f(t,u,u^′)=0, t∈(0,1), subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems.