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I consider a stochastic optimization problem for a time-changed Besselprocess 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 thechoice of diffusion rate in order to maximize the chance of hitting aninfinitesimal region around the origin at a set time in the future. Moreprecisely, the parameter associated with "the chance of hitting the origin" isthe exponent for a singularity induced at the origin of the final timeprobability density. I show that the optimal exponent solves a transcendentalequation depending on the ratio $\frac{r_{2}}{r_{1}}$ and the dimension of theBessel process.

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