Path dependent equations driven by Hölder processes

This article investigates existence results for path-dependent differential equations driven by a Hölder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder theorem and the vector field is allowed to be unbounded. The Hölder function is typically the trajectory of a stochastic process.     

几何平均下的水平重置期权定价

针对重置期权的风险对冲△跳现象,研究了一种亚式特征的水平重置期权的定价问题.首先在BS模型下用股票的几何平均价格作为水平重置期权执行价格重置与否的统计量,然后运用测度变换和鞅定价方法得到了风险中性定价公式,最后利用风险中性定价公式得出风险对冲△值的显示解,改进了水平重置期权的部分已有结果.     

On the Somigliana dislocations associated with applications of the Neuber–Papkovich solution in multiply-connected regions

Summary The study aims to explain the problem of single-valuedness of the mean stress and dilatation in multiply-connected regions. It is shown that in multiply-connected regions, displacement representation potentials, in particular the Neuber–Papkovich potentials, have to be submitted to the integral conditions in order to avoid the many-valuedness. Received 8 September 1998; accepted for publication 8 April 1999     

资产跳跃下CM策略多期收入保证价格模拟

恒定混合策略(CM策略)多期收入保证价格是保本基金发行方采取设置止损的CM\linebreak策略作为投资策略时收取保 本费的理论依据, 其中标的资产由复合泊松过程和维纳过程共同驱动, 这一定价问题内嵌奇异期权, 蒙特卡罗模拟方法擅长处理这种高维数量金融问题. 基于风险中性测度推导出多期收入保证价格的现值表达式, 用条件蒙特卡罗推导出这一现值表达式的模拟公式. 在给定参数下分别用普通蒙特卡罗和条件蒙特卡罗计算CM策略多期收入保证价格的数值解, 结果显示两种蒙特卡罗方法均能有效计算其数值解, 之后通过给定显著性水平下的置信区间长度评价两种方法的精确度, 结果显示条件蒙特卡罗比普通蒙特卡罗有很大改进. 接着运用条件蒙特卡罗模拟研究多期收入保证价格对不同参数范围的变化情况.     

Analog simulation of a simple system with state-dependent diffusion

We have constructed an electronic simulator of a simple bistable system driven by noise, whose intensity is determined by the instantaneous value of the coordinate. We observe that the most probable state of the system can be reversed by altering the noise intensity only in the neighborhood of the barrier, an effect pointed out by Landauer many years ago in the context of discussions on entropy-related stability criteria for nonequilibrium systems. We compare detailed measurements on the system with the recent white noise calculations of Landauer and van Kampen. The system also has interesting possibilities for tests of contemporary colored noise theory which we illustrate with an example.