供应商回购承诺下的销售商存货质押融资决策

研究由一个供应商和销售商组成的供应链。销售商为中小企业,在受资金约束时无法通过自身信用获得所需融资,此时供应商可以为销售商贷款提供担保以提高其融资授信额度。本文采用销售商违约后剩余质押物的回购率来衡量供应商对融资风险的分担程度,对参与各方的存货质押融资决策进行了深入研究。结果表明:供应商的回购承诺提高了银行利润,在一定条件下提高了银行的质押率;并且,有回购承诺的融资决策在市场前景乐观情况下可以有效缓解销售商的融资困境。     

Optimal investment–consumption problem: Post-retirement with minimum guarantee

We study the optimal investment–consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover, to have a minimum guarantee for the final annuity, a safety level for the wealth process is considered. To solve the stochastic optimal control problem via dynamic programming, we obtain a Hamilton–Jacobi–Bellman (HJB) equation on a bounded domain. The existence and uniqueness of classical solutions are proved through the dual transformation. We apply the finite difference method to find numerical approximations of the solution of the HJB equation. Finally, the simulation results for the optimal investment–consumption strategies, optimal wealth process and the final annuity for different admissible ranges of consumption are given. Furthermore, by taking into account the market present value of the cash flows before and after the annuitization, we compare the outcomes of different scenarios.     

Victory Tax: A Holistic Income Tax System

How can an income tax system be designed to exploit human nature and a free market to create a poverty free society, while balancing budgets without disproportional tax burdens? Such a tax system, with universal character, is deduced from the following guiding principles: (1) a single tax rate applies to all income types and levels; (2) the tax rate adjusts to satisfy budget projections; (3) government transfer only supplements the income of households with self-generated income below the poverty line; (4) deductions for basic living expenses, itemized investments and capital losses are allowed; (5) deductions cannot be applied to government transfer. A general framework emerges with three parameters that determine a minimum allowed tax deduction, a maximum allowed itemized deduction, and a maximum deduction defined by income percentage. An income distribution that mimics the United States, and a series of log-normal distributions are considered to quantitatively compare detailed characteristics of this tax system to progressive and flat tax systems. To minimize government dependency while maximizing after-tax income, the effective tax rate (ETR) as a function of income percentile takes the shape of the letter, V, inspiring the name victory tax, where the middle class has the lowest ETR.     

面向任务保障的多组件系统效益优化策略

为了保障系统在执行任务期间高可靠、高效益的运行,从系统效益的角度出发,构建了系统可靠性模型,采用边际效应思想构建了效益重要度,提出了一种面向任务保障的多组件系统效益优化策略。当系统可靠度下降到设定阈值时,计算系统各组件的效益重要度,选择效益重要度最大的组件进行备件分配,如此进行迭代,直到完成任务保障,形成最优的备件分配序列。通过该策略实现了以运行效益最优为目标,以系统可靠度和任务保障时长为约束的备件分配序列。最后,通过数值仿真验证了该策略的可行性。     

具有一般关联结构母子公司担保债券的定价和风险分析

为更好地处理母子公司担保条款对公司债券估值的影响，在随机利率服从CIR模型下，分析了一家母公司同时为n家子公司提供担保的公司债券定价问题。通过一家母公司与n家子公司违约强度的关联结构描述因担保而形成的母子公司违约关联结构，采用约化方法，建立了具有一般结构母子公司担保债券定价的数学模型，得到了定价公式。分析了母公司为n家子公司提供担保所体现的担保价值和可能引发的违约传染性风险。结果表明，母子公司担保条款提升了子公司的信用等级，但同时也可能引发违约传染，导致母公司违约概率增加。     

求解非减上模集函数最小值问题的近似算法及其性能保证

上模集函数的优化问题在组合优化问题中有广泛应用,许多组合优化问题,如设备选址问题、p-中心问题等都可化为上模集函数的优化问题.本文给出了求解非减上模集函数最小值问题的一种近似算法,并讨论了所给算法的性能保证.     

Approximation algorithms for the test cover problem

In the test cover problem a set of m items is given together with a collection of subsets, called tests. A smallest subcollection of tests is to be selected such that for each pair of items there is a test in the selection that contains exactly one of the two items. It is known that the problem is NP-hard and that the greedy algorithm has a performance ratio O(log m). We observe that, unless P=NP, no polynomial-time algorithm can do essentially better. For the case that each test contains at most k items, we give an O(log k)-approximation algorithm. We pay special attention to the case that each test contains at most two items. A strong relation with a problem of packing paths in a graph is established, which implies that even this special case is NP-hard. We prove APX-hardness of both problems, derive performance guarantees for greedy algorithms, and discuss the performance of a series of local improvement heuristics. Partially supported by the Future and Emerging Technologies Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).Partially supported by a Merck Computational Biology and Chemistry Program Graduate Fellowship from the Merck Company Foundation.Also Iceland Genomics CorporationPartially supported by subcontract No. 16082-RFP-00-2C in the area of ``Combinatorial Optimization in Biology (XAXE),' Los Alamos National Laboratories, and NSF grant CCR-0105548.Mathematics Subject Classification: 90B27