On the approximation by the continuous time models

这个项目的目的是进行一项实验，以测试应用最优序贯检验来确定正态均值的符号的能力，作为解决一大类序贯检验问题的近似。如果这种近似被证明是有效的，那么它的两个潜在优势是：它很容易计算，并且可以简单地用一条易于解释的曲线来表示，确定最佳的停止时间。顺便说一句，该曲线的一个版本是其中停止的正常显著水平被表示为迄今所获得的信息的函数。实验包括将近似与用于正态分布的标准差超过1的序贯检验的最优贝叶斯解进行比较。在这个问题中，假设θ=σ-2的未知值服从伽马分布。中心极限定理的天真应用给了我们不令人满意的逼近。对于离散时间过程，我们将Edgeworth型近似与连续时间近似结合起来考虑。数值计算尚未得到令人满意的结果。Hogan(1986，Ann)提出的常数。统计学家。)本文考虑的另一个问题是指数平方根曲线边界淘汰型欧式期权的定价问题。我们已经得到了定价公式，其中的一部分已经发表(Morimoto，M1999，波士顿大学博士论文)。

The object of this project is to carry out an experiment on the ability to apply the optimal sequential test for determining the sign of a normal mean as an approximation to the solution of a large class of sequential testing problems. Two potential advantages of such an approximation, if it is proved to be effective, are that it is easy to calculate and that it can be expressed simply in terms of a single easily interpreted curve, determine the optimal stopping time. Incidentally one version of that curve is one where a normal significance level for stopping is expressed as a function of the information obtained to date.The experiment consists of comparing the approximation to the optimal Bayes solution for the sequential test that the standard deviation of a normal distribution exceeds one. In this problem the unknown value of θ = σ-2 is assumed to have a gamma distribution. The naive application of the central limit theorem gives us unsatisfactory approximations. The Edgeworth type approximation has been considered together with the continuous time approximation for the discrete time processes. The numerically satisfactory results have not been obtained yet. The constant proposed by Hogan (1986, Ann. Statists.) is obtained for the gamma random walk.Another problem considered in this project is the pricing of the exponentially square root curved boundary knockout type European type option. We have obtained the pricing formula, a part of which has been published (Morimoto, M 1999, Ph.D. thesis Boston University).