New developments of estimations and numerical analysis in finance

在数理金融学中，估计和数值分析主要有三个方面的研究。1.从理论上给出了贝叶斯估计对多个数据的逼近的真实的收敛速度和逼近参数的选择。同时研究了滤波在期望效用最大化问题中的作用。2.利用Malliavin演算，给出了分数布朗运动金融模型下的风险测度Greeks，并数值验证了其效果。3.研究了日本股票市场跳跃的存在性及其分布的估计。还研究了资产泡沫的存在。

Three main studies on estimations and numerical analysis in mathematical finance were considered. 1. A convergence rate to the real value of an approximation of the Bayesian estimator with respect to a number of data and choice of approximating parameters were theoretically given. Effects of filtering in expected utility maximization problems were also studied. 2. Using the Malliavin calculus, Greeks, which is one of risk measure, under a financial model with fractional Brownian motions were given and some effects were numerically confirmed. 3. Existence of jumps in Japanese stock markets and estimations of the distribution were studied. Existence of asset bubbles was also studied.