Using a geometric Brownian motion to control a Brownian motion and vice versa

被引：4
|
作者：
Lefebvre, M
机构：
[1] Departement de M., Ecole Polytech. de Montreal, Montréal, Que. H3C 3A7, C.P. 6079, Succursale Centre-ville
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1997年 / 69卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
stochastic optimal control; homing problem; Riccati equation; hitting time;
D O I：
10.1016/S0304-4149(97)00040-9
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let x(t) be a one-dimensional Brownian motion. The homing problem for a controlled x(t) process is solved by using a mathematical expectation for an uncontrolled geometric Brownian motion. Furthermore, it turns out that the optimally controlled process is a Bessel process. Similarly, a geometric Brownian motion is optimally controlled by using a mathematical expectation for an uncontrolled Brownian motion process. (C) 1997 Elsevier Science B.V.
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页码：71 / 82
页数：12
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