Open Access
Translator Disclaimer
2014 Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time
Jeremy Clark
Author Affiliations +
Electron. Commun. Probab. 19: 1-19 (2014). DOI: 10.1214/ECP.v19-2846

Abstract

I consider a stochastic optimization problem for a one-dimensional continuous martingale whose diffusion rate is constrained to be between two positive values $r_{1}<r_{2}$. 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 $\frac{r_{2}}{r_{1}}$.

Citation

Download Citation

Jeremy Clark. "Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time." Electron. Commun. Probab. 19 1 - 19, 2014. https://doi.org/10.1214/ECP.v19-2846

Information

Accepted: 26 July 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60153
MathSciNet: MR3246967
Digital Object Identifier: 10.1214/ECP.v19-2846

JOURNAL ARTICLE
19 PAGES


SHARE
Back to Top