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The main results are as follows:We review the existing Monte Carlo control variates estimators of the price of Asian options and propose a new one. According to pratical needs, we define efficiency as the inverse of the product of the variance of an estimator and its computational time and make it a standard for comparisons to draw the following conclusions: Firstly, the more control variates correlate with arithmetic average Asian options, the larger is the efficiency of an estimator with these control variates, but among which the geometric average option plays the most important role; Secondly, an estimator with more control variates is better than one with less ones only when the time to maturity is long and the volatility is high.

在综合已有研究工作的基础上,本论文的主要创新成果如下:(1)我们回顾了已有的亚洲期权价格的蒙特卡罗控制变量估计,并提出了一个新的控制变量估计,且从客观实际出发,将估计值的方差和计算时间的乘积的倒数定义为效率并以它为标准比较各估计,得到以下结论:与算术平均亚洲期权相关程度越大的控制变量构成的估计的效率越大,而其中起主要作用的控制变量为几何平均亚洲期权的价格;只有在到期时间较长且标的资产的波动率较大时,元素多的多元控制变量估计比元素少的效率大。

4Based on a fact that the price formula of Asian options can be transformed into that of vanilla European option when the time to maturity is less than or equal to the length of average, we skillfully obtain the analytical price formula for the option on the minimum or the maximum of two geometric average prices and generalize it to obtain the price formula of several average prices for the first time. We also apply the method of [121], which approximates the arithmetic average by the geometric average, to the pricing of opitons on the minimum or the maximum of two arithmetic average prices to obtain Its approximated price formula. Numerical results show that the approximated price is relatively accurate when the riskless interest rate is large or the option is in the money and the volatility of two underlying assets are high and its accuracy is a little reduced but still good when the dividends are considered. However, it is hardly affected by the sampling number.

我们基于观察到的一个事实即当离到期时间小于或等于平均期间时亚洲期权的价格可变换成普通的欧式期权的价格,从而巧妙地得到了两个几何平均价格的最小或最大值期权价格的解析公式,通过简单地推广,首次得到了多个几何平均时的价格公式;将[121]用于算术平均亚洲期权的定价方法推广到两个算术平均价格的最小或最大值期权,从而得到它的渐进公式,数值结果表明:渐进价格的准确性在无风险利率较大或期权为实值且两标的资产的波动率较小时较好,抽样的个数对它没有影响,但考虑红利时它稍有下降但仍较好。

The terms indebtedness and obligations are (hereinafter collectively referred to as the Obligations) used herein in their most comprehensive sense and include any and all advances, debts, obligations and liabilities of Seller, heretofore, now, or hereafter made, incurred or created, whether voluntarily or involuntarily, and however arising(including, without limitation, indebtedness owing by Seller to third parties who have granted Buyer a security interest in the accounts, chattel paper and general intangibles of said third party; and further including, without limitation, any and all attorneys fees, expenses, costs, premiums, charges and interest owed by Seller to Buyer, whether under the Agreements, or otherwise) whether due or not due, absolute or contingent, liquidated or unliquidated, determined or undetermined, whether Seller may be liable individually or jointly with others, whether recovery upon such indebtedness may be or hereafter becomes barred by any statute of limitations or whether such indebtedness may be or hereafter becomes otherwise unenforceable, and includes Sellers prompt, full and faithful performance, observance and discharge of each and every term, condition, agreement, representation, warranty undertaking and pro visio n to be performed by Seller under these Agreements.

这里的术语"负债""债务"应按照各自最广泛的含义被使用,债务包括卖方先前、现在和今后,基于自愿或非自愿发生的所有预付款、负债、债务和责任,不论债务如何产生,(包括但不限于,卖方对已用自己的帐户、动产文书或一般无体物向买方提供担保利益的第三方之负债,并进而包括但不限于,卖方在协议等项下欠付买方的全部律师费、支出、费用、保险费、运费和利息),不论债务是否已经到期、是否必然发生、是否已清算、是否已决,不论卖方是单独或与他人连带承担责任,不论债务的追偿是否已经或将会受到时效法的阻碍,也不论债务是否已经或将要无法强制执行,卖方应当即时、充分和善意的履行、遵守和完成全部条款、条件、协议、陈述、担保义务和这些协议项下卖方应当履行的条款。

Whether due or not due, absolute or contingent, liquidated or unliquidated, determined or undetermined, whether Seller may be liable individually or jointly with others, whether recovery upon such indebtedness may be or hereafter becomes barred by any statute of limitations or whether such indebtedness may be or hereafter becomes otherwise unenforceable, and includes Sellers prompt, full and faithful performance, observance and discharge of each and every term, condition, agreement, representation, warranty undertaking and provision to be performed by Seller under these Agreements.

这里的术语"负债""债务"应按照各自最广泛的含义被使用,债务包括卖方先前、现在和今后,基于自愿或非自愿发生的所有预付款、负债、债务和责任,不论债务如何产生,,不论债务是否已经到期、是否必然发生、是否已清算、是否已决,不论卖方是单独或与他人连带承担责任,不论债务的追偿是否已经或将会受到时效法的阻碍,也不论债务是否已经或将要无法强制执行,卖方应当即时、充分和善意的履行、遵守和完成全部条款、条件、协议、陈述、担保义务和这些协议项下卖方应当履行的条款。

Including, without limitation, indebtedness owing by Seller to third parties who have granted Buyer a security interest in the accounts, chattel paper and general intangibles of said third party; and further including, without limitation, any and all attorneys fees, expenses, costs, premiums, charges and interest owed by Seller to Buyer, whether under the Agreements, or otherwise) whether due or not due, absolute or contingent, liquidated or unliquidated, determined or undetermined, whether Seller may be liable in华夏学习网idually or jointly with others, whether recovery upon such indebtedness may be or hereafter becomes barred by any statute of limitations or whether such indebtedness may be or hereafter becomes otherwise unenforceable, and includes Sellers prompt, full and faithful performance, observance and discharge of each and every term, condition, agreement, representation, warranty undertaking and provision to be performed by Seller under these Agreements.

这里的术语"负债""债务"应按照各自最广泛的含义被使用,债务包括卖方先前、现在和今后,基于自愿或非自愿发生的所有预付款、负债、债务和责任,不论债务如何产生,(包括但不限于,卖方对已用自己的帐户、动产文书或一般无体物向买方提供担保利益的第三方之负债,并进而包括但不限于,卖方在协议等项下欠付买方的全部律师费、支出、费用、保险费、运费和利息),不论债务是否已经到期、是否必然发生、是否已清算、是否已决,不论卖方是单独或与他人连带承担责任,不论债务的追偿是否已经或将会受到时效法的阻碍,也不论债务是否已经或将要无法强制执行,卖方应当即时、充分和善意的履行、遵守和完成全部条款、条件、协议、陈述、担保义务和这些协议项下卖方应当履行的条款。

Including, without limitation, indebtedness owing by Seller to third parties who have granted Buyer a security interest in the accounts, chattel paper and general intangibles of said third party; and further including, without limitation, any and all attorneys fees, expenses, costs, premiums, charges and interest owed by Seller to Buyer, whether under the Agreements, or otherwise) whether due or not due, absolute or contingent, liquidated or unliquidated, determined or undetermined, whether Seller may be liable individually or jointly with others, whether recovery upon such indebtedness may be or hereafter becomes barred by any statute of limitations or whether such indebtedness may be or hereafter becomes otherwise unenforceable, and includes Sellers prompt, full and faithful performance, observance and discharge of each and every term, condition, agreement, representation, warranty undertaking and pro visio n to be performed by Seller under these Agreements.

这里的术语"负债""债务"应按照各自最广泛的含义被使用,债务包括卖方先前、现在和今后,基于自愿或非自愿发生的所有预付款、负债、债务和责任,不论债务如何产生,(包括但不限于,卖方对已用自己的帐户、动产文书或一般无体物向买方提供担保利益的第三方之负债,并进而包括但不限于,卖方在协议等项下欠付买方的全部律师费、支出、费用、保险费、运费和利息),不论债务是否已经到期、是否必然发生、是否已清算、是否已决,不论卖方是单独或与他人连带承担责任,不论债务的追偿是否已经或将会受到时效法的阻碍,也不论债务是否已经或将要无法强制执行,卖方应当即时、充分和善意的履行、遵守和完成全部条款、条件、协议、陈述、担保义务和这些协议项下卖方应当履行的条款。

The carrier' s liability shall be that of warehouseman, only for loss, damage, or delay caused by fire occurring after the expiration of the free time allowed by tariffs lawfully on file (such free time to be computed as therein provided) after notice of the arrival of the property at destination or at the port of export has been duly sent or given, and after placement of the property for delivery at destination, or tender of delivery of the property to the party entitled to receive it, has been made.

承运人的责任等同于仓库业者的责任,仅对在运费表规定的免费时间(此免费时间运费表的规定计算)到期,且正式发出或收到货物抵达目的地或出口港的通知,在目的地做好交货准备,或提出将货物提交有权认领货物的当事人之后,因发生火灾而造成的灭失、损失或延误负责。

The apprenticeship and qualification contract schemes have proven a particularly effective means of significantly and durably improving the employability of lowskilled workers, in part because of their significant reliance on co-financing on the part of both employers and employees.

而且,提高青年就业率还具有缓解养老金负担的好处。在追加的福利交纳金刚好在预计的运营赤字将最迅速上升的时候滚滚而来的同时,与此相关的养老金费用在本世纪中叶前还尚未到期,而那时预计系统的均衡正在不断地得到改善。

Having failed to secure enough funding to cover maturing loans on stock options taken out to fund the takeover bid of VW, Wiedeking's departure is being seen as an acceptance of blame for Porsche's worsening financial situation--the result of what many financial-industry experts describe as overambitious growth targets.

因对于用于大众的接管企业出价的期权的已到期贷款,未能提供足够的资金偿付,wiedeking的离去被视作是保时捷日薄西山的财政状况的引咎之举,其后果为众多金融业监管专家描述为&眼高手低的苦根&。

Reviewing website of 7 years, my that half-dead station Www.20592.com expires because of the domain name overlooked add cost, this ought to be my fault, the birthday that connects it gives misremembered, be punished Google is PR value from 4 fell 2, other is worth twice with the PR of his station also from 3 fell 1, baidu is collected became inside a few days 1, without language ah how saying again also is a year of much painstaking effort, and return complicity other a few new stations!

回顾着07年的网站,我的那半死不活的站www.20592.com因为域名到期忘记了续费,这应当是我的错,连它的&生日&都给记错了,受到惩罚便Google是PR值从4降到了2,其它两个和他一起的站的PR值也从3降到了1,百度收录几天内变成了1,无语呀再怎么说也是一年多的心血,而且还连累了其它几个新站!

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