鞅

Martingal ; transaction costs ; portflio ; admissible strategy

鞅； 交易费；投资策略；可容许策略

We study the relationship of martingale and arbitrage in securities markets with transaction costs and solvency in this paper, and obtain some significative results.

对带有交易费用和偿付约束的金融市场套利与鞅的关系问题进行了研究，得到了一些有意义的结果。

On the basis of the theory of option pricing,We study the connection between America call option and European call option;Under the assumption condition of Black-Scholes formula ,use the theory of martingales and stopping time,get the conclusion that: the price of America call option equals the price of European call option; Discuss some numeric computing methods of the put America option pricing, with the invarional inequaility for optimal stopping, prove the boundary property of America put option price ...

基于期权定价的基本理论，研究美式看涨期权与欧式看涨期权之间的关系；在Black-Sc holes公式假设条件下，利用鞅和停时理论，得美式看涨期权的价格与欧式看涨期权的价格相等；探讨美式看跌期权价格的数字化计算，在相关假设条件下，利用基于最优化时的变分不等式证明了美式看跌期权价格的有界性，并介绍了几种美式看跌期权价格的数字化计算方法。

Based on the new theories developed in biology,the basic theoreticalproblems of the genetic algorithm,which are the representation scheme,co-nvergence and convergence rates of the genetic algorithms,etc.,are discussedwith Boolean algebra,group theory,martingale theory and axiomatic method inthe framework of the Markov chain.

本文以生物学发展的新理论为背景，在遗传算法的Markov链框架下运用Boole代数、群、鞅及公理化方法研究遗传算法的表示、收敛性与收敛速度等基本理论问题。

Inequalities of martingales play an important role in modern martingale theory.

中文摘要：在现代鞅论中，鞅不等式具有很重要的作用。

The basic thought is that the functions or martingales among the spaces are made linearly up with a kind of very simple functions or martingales.

其基本思想是将所讨论的空间中的函数或鞅用一类十分简单的函数或鞅经线性组合生成。

This thesis is devoted to the study of 〓-type inequalities for martingales,such as the maximal inequalities,the inequalities for square functions,the inequali-ties for martingale transforms,the inequalities for singular integrals.

第三章证明了关于Hardy平均算子〓的双〓不等式、双〓凸引理，并通过考虑鞅的重排不等式，建立了鞅的双〓均方函数不等式、条件均方函数不等式，给出了这类不等式成立的一个充分必要条件。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

基于这个分解，证明了树鞅指标集同构于一个有向森林，这个森林中的每一棵树都是有向局部有限树，这就证明了树鞅指标集有一个分解，它的每一部分同构于一个有向无限、局部有限树。

This paper summarizes the research job of predecessors, full text is divided in four part:The first part introduces the develop history and present conditions of MCRE;In the second part, the concept of average Markov process is introduced. Moreover we investigate the relations for Markov processes, martingales, stationary processes and average Markov process systematically.The third part summarizes the model that constructs the MCRE by p-m chains and skew product Markov chains by p-m chains, also we discuss the relations among the basic gunctions of the probability character for MCREIn the fourth part, we discuss the dimension of GW-tree and the canonical branching chain in random environment, furthermore we summarize the exact formulas of mathematical expectation and variance of branching chain in random environment.

本文主要是综述这方面前人工作，全文分成四个部分：第一部分介绍了MCRE的发展历史和研究现状；第二部分研究了马氏过程、鞅和平稳过程这三类经典的随机过程的相互关系，包括他们之间的包含和排斥关系，引入了&均马氏过程&的概念，研究了它与三类经典过程—马氏过程、鞅及平稳过程的关系；第三部分综述了用p-m链构造的构造的随机环境中的马氏链和绕积马氏链，讨论了与之相关的概率特性函数的性质；第四部分讨论了GW树的维数，并综述了随机环境中的典范的分枝链，讨论了随机环境中的分枝链的数学期望和方差的计算公式。

In the end, we find a martingale, by which we get some measures of the severity of ruin in the continous time compound binomial model.

并找了一个鞅，利用这个鞅算出了连续时间复合二项模型中，从破产到第一次恢复的时间，恢复的损失以及有关的期望等度量。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。