First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries

作     者：Zhen YU Mao Zai TIAN Zhen YU;Mao Zai TIAN

作者机构：Center for Applied StatisticsSchool of StatisticsRenmin University of ChinaBeijing 100872P.R.China School of Mathematics and Data ScienceChangji UniversityChangji 831100P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第6期

页      面：1505-1520页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by the Fundamental Research Funds for the Central Universities the Research Funds of Renmin University of China(Grant No.22XNL016) 

主　　题：Boundary non-crossing probability first density passage density two-sided piecewise continuous boundaries Brownian motion 

摘      要：The first passage time has many applications in fields like finance,econometrics,statistics,and ***,explicit formulas for the first passage density have only been obtained for a few *** paper derives an explicit formula for the first passage density of Brownian motion with twosided piecewise continuous boundaries which may have some points of *** are used to obtain a simplified formula for estimating the first passage ***,the results are also generalized to the case of two-sided general nonlinear *** can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density.