方阵化零多项式的几点应用

对给定的方阵,探讨其化零多项式的如下应用:辅助判断方阵可否对角化,当其可对角化时,给出相应对角阵的结构;判断方阵任意多项式的可逆性,当其可逆时,给出求逆矩阵的统一方法。     

公差原则中最小实体要求问题初析

扼要地对ＧＢ／Ｔ１６６７１－１９９６标准中规定的最小实体要求内容的提出，概念，应用作初步探析。     

Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes

In a market driven by a Lévy martingale, we consider a claim ξ. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for ξ: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives, and the corresponding versions of the Clark-Haussmann-Ocone theorem.     

Exponential Hedging and Entropic Penalties

We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X . We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relative entropy minus a correction term involving B or maximize the Q -price of B subject to an entropic penalty term. Our result is robust in the sense that it holds for several choices of the space of hedging strategies. Applications include a new characterization of the minimal martingale measure and risk-averse asymptotics.     

基于改进最小方差法的汽车整车企业竞争力动态评价

国内外较少有文献对“汽车整车企业竞争力”进行动态综合评价,而动态性是竞争力的显著特征;针对这一情况,利用改进最小方差法对2010-2014年沪深两市22家汽车整车企业竞争力进行动态综合评价;结合K-Means聚类分析方法将企业分为竞争力较强、中等及较弱3类,并对分类结果进行分析;研究表明：改进最小方差法能够兼顾时间信息的稳定度及丰富度,可推广性强。     

MINIMAL ENTROPY–HELLINGER MARTINGALE MEASURE IN INCOMPLETE MARKETS

This paper defines an optimization criterion for the set of all martingale measures for an incomplete market model when the discounted price process is bounded and quasi-left continuous. This criterion is based on the entropy–Hellinger process for a nonnegative Doléans–Dade exponential local martingale. We develop properties of this process and establish its relationship to the relative entropy "distance." We prove that the martingale measure, minimizing this entropy–Hellinger process, is unique. Furthermore, it exists and is explicitly determined under some mild conditions of integrability and no arbitrage. Different characterizations for this extremal risk-neutral measure as well as immediate application to the exponential hedging are given. If the discounted price process is continuous, the minimal entropy–Hellinger martingale measure simply is the minimal martingale measure of Föllmer and Schweizer. Finally, the relationship between the minimal entropy–Hellinger martingale measure (MHM) and the minimal entropy martingale measure (MEM) is provided. We also give an example showing that in contrast to the MHM measure, the MEM measure is not robust with respect to stopping.     

Periodical Preventive-Maintenance Contract for a Leased Facility with Weibull Life-Time

This paper develops a mathematical model to derive the optimal periodical preventive maintenance (PM) policy for a leased facility with Weibull life-time. Within a lease period, any failures of the facility are rectified by minimal repairs and a penalty may occur to the lessor when the time required to perform a minimal repair exceeds a reasonable time limit. To reduce failures of the facility, additional PM actions are carried out periodically during the lease period. When the life-time distribution of a product is Weibull, the optimal number of PM actions and the corresponding maintenance degrees are derived such that the expected total maintenance cost is minimized. The structural properties of the optimal policy are investigated and an efficient algorithm is provided to search for the optimal policy. Finally, numerical examples are provided to illustrate the features of the proposed model.