文章基本信息

标题：Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time
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作者：Clark, Jeremy Thane
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2014
卷号：19
页码：1-19
DOI：10.1214/ECP.v19-2846
语种：English
出版社：Electronic Communications in Probability
摘要：I consider a stochastic optimization problem for a one-dimensional continuous martingale whose diffusion rate is constrained to be between two positive values $r_)<r_,$. The problem is to find an optimal adapted strategy for the choice of diffusion rate in order to maximize the chance of hitting an infinitesimal region around the origin at a set time in the future. More precisely, the parameter associated with "the chance of hitting the origin" is the exponent for a singularity induced at the origin of the final time probability density. I show that the optimal exponent solves a transcendental equation depending on the ratio $\frac{r_,}{r_)}$.