New developments of estimations and numerical analysis in finance

金融估计和数值分析的新进展

• 批准号: 23740089
• 负责人: YASUDA Kazuhiro
• 金额: $ 2.41万
• 依托单位: Hosei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740089/
• 关键词: フィルタリング; フラクショナルブラウン運動; マリアヴァン解析; グリークス; Malliavin解析; 局所マルチンゲール; 数理ファイナンス; Greeks; 統計解析

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.

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。

项目成果

On Effects of Estimations and Information for Expected Log-Utility Maximization Problems

• DOI: 10.5687/sss.2014.90
• 发表时间: 2014-05
• 作者: Y. Asakura

Some Numerical Results of Sensitivity Analysis for Expected Values w.r.t. Linear SDE with Long Memory

预期值的敏感性分析的一些数值结果

• 发表时间: 2012
• 期刊: Proceedings of the 43th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
• 作者: Hidetomo Nagai;K. Yasuda
• 通讯作者: K. Yasuda

Strong consistency of Bayesian estimator under discrete observation and unknown transition density

离散观测和未知转移密度下贝叶斯估计的强一致性

• DOI: 10.1007/978-3-0348-0097-6_10
• 发表时间: 2011
• 期刊: Progress in Probability
• 作者: A. Kohatsu-Higa;N. Vayatis;K. Yasuda
• 通讯作者: K. Yasuda

不連続ドリフト係数を持つ確率微分方程式の弱近似について

具有不连续漂移系数的随机微分方程的弱近似

• 发表时间: 2013
• 作者: Xuefeng Liu;Michael Plum and Shin'ichi Oishi;田端正久，野津裕史;安田和弘
• 通讯作者: 安田和弘

Sensitivity Analysis of Expectation with respect to Stochastic Differential Equations with Long Memory through Malliavin Calculus

基于Malliavin微积分的长记忆随机微分方程期望的敏感性分析

• 发表时间: 2012
• 期刊: Transactions of the Institute of Systems, Control and Information Engineers
• 作者: 長井秀友;K. Yasuda
• 通讯作者: K. Yasuda