A VARIATIONAL APPROACH TO OPTIMAL STOPPING PROBLEMS FOR DIFFUSION PROCESSES

被引：4

作者：

Arkin, V. I. ^{[1
]}

Slastnikov, A. D. ^{[1
]}

机构：

[1] RAS, CEMI, Moscow 117418, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2009年 / 53卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

diffusion process; optimal stopping; variational approach; smooth pasting; two-dimensional geometric Brownian motion; Stefan problem;

D O I：

10.1137/S0040585X97983766

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：

We describe a variational approach to the solution to optimal stopping problems for diffusion processes as an alternative to the traditional approach based on the solution of the Stefan (free-boundary) problem. The connection of this variational approach to smooth pasting conditions is established. We present an example where the solution to the Stefan problem is not the solution to an optimal stopping problem. On the basis of the proposed approach, we obtain the solution to an optimal stopping problem for a two-dimensional geometric Brownian motion with a homogeneous payoff function.

引用

页码：467 / 480

页数：14

共 15 条

[1] On the smooth-fit principle in Rn [J].