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


 
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1. Title Title of document Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time
 
2. Creator Author's name, affiliation, country Jeremy Thane Clark; Michigan State University; United States
 
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4. Description 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 $\frac{r_{2}}{r_{1}}$.
 
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7. Date (YYYY-MM-DD) 2014-07-26
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2846
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-2846
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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