鞅

In this paper, it is proved the complete convergence of series of dependent random variables by making a convergent martingale.

本文通过构造收敛鞅，证明了相依随机变量序列的完全收敛性。

The thesis studies the tree martingale theory and their applications,which hasa broadly applied background.

本课题研究树鞅与相关领域的联系及其应用，这个课题是带有应用背景的理论研究。

In the martingale case, our locally risk-minimizing strategy reduces to Moller[5]s one.

在鞅的情形中，我们的局部风险最小对冲策略简化为Moller[5]的风险最小对冲策略。

Proper attention should be paid to Shangyang's obscurant thought in the circle of scholars because it had profoundly affected culture,thought and politics throughout the history of China's feudal societies.

商鞅的愚民思想对中国封建社会的政治思想文化产生过长远而又深刻的影响，应当引起学术界的重视。

With the application of stochastic optimal control theory and martingale optimality principle, the optimal solutions of the models in explicit form are extracted.

运用随机最优控制理论及鞅最优性原理求出了模型的显式最优解。

First,making use of martingale method,pricing formula on European contingent claim,price of call and put option were obtained

首先利用鞅方法给出欧式未定权益一般定价公式，并得到欧式买权、卖权价格的解析表达式及平价关系，推广了一般 Black- Scholes模型及 Merton模型的结果

Using martingale method, we deal with option pricing problems on foreign currency, and obtain price expression of European call and put option under stochastic interest rate and their parity. We also consider hedging problems of options.

在随机利率情况下，利用鞅方法讨论了外汇欧式期权的定价问题，得到了欧式看涨期权和看跌期权价格的解析表达式及其评价关系，并考虑了期权的套期保值问题。

First,making use of martingale method,pricing formula on European contingent claim,price of call and put option were obtained;Then the partial differential equation which price of European contingent claim satisfgied was deal with and hedging strategy for option was obtained.The sensitivity analysis was given.

首先利用鞅方法给出欧式未定权益一般定价公式，并得到欧式买权、卖权价格的解析表达式及平价关系，推广了一般Black-Scholes模型及Merton模型的结果；其次利用Ito公式给出欧式未定权益价格应满足的偏微分方程和套期保值策略；最后给出了欧式期权价格的灵敏度分析。

The notion of sample relative entropy , as a random measure of the deviation of a sequence of nonnegative continuous random sequence from independent random sequence with exponential distribution, is introduced.

利用样本相对熵作为一般非负连续型随机变量序列相对于服从指数分布的独立但不同分布随机变量序列偏差的一种随机性度量，运用鞅理论及分析方法，研究了一类随机变量序列加权和的用不等式表示的极限定理，即强偏差定

In this paper, we discuss the estimate of regression function in nonparametric regression model based on exponential in tegral mart in gale difference.

摘要本文研究了误差项是鞅差序列，且满足某种指数矩条件的非参数回归函数的估计。

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。