How to cite item

Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time

   
@article{ECP2846,
	author = {Jeremy Clark},
	title = {Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {},
	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 $\frac{r_{2}}{r_{1}}$.},
	pages = {no. 48, 1-19},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-2846},    
        url = {http://ecp.ejpecp.org/article/view/2846}}