Document Type
Lecture
Publication Date
10-23-2014
Abstract
I consider a stochastic optimization problem for a time-changed Brownian motion whose diffusion rate is constrained to be between two positive values r₁ < r₂. 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 of r₂ to r₁. Without going into technical details, some ideas behind this technique will be illustrated in the case of a model of squared Bessel nonintersecting paths.
Relational Format
presentation
Recommended Citation
Clark, Jeremy, "Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time" (2014). Analysis Seminar. 11.
https://egrove.olemiss.edu/math_analysis/11
