Optimal prediction of the last-passage time of a transient diffusion

Kristoffer Glover and Hardy Hulley ()
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Hardy Hulley: Finance Discipline Group, University of Technology Sydney, https://profiles.uts.edu.au/hardy.hulley

Published Paper Series from Finance Discipline Group, UTS Business School, University of Technology, Sydney

Abstract: We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance from the last-passage time $\gamma_z$ associated with a given level $z>0$, for an arbitrary nonnegative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$ is in fact the first time that $X$ assumes a value outside a half-open interval $[0,r_*)$. The upper boundary $r_*>z$ of this interval is characterized either as the solution for a one-dimensional optimization problem, or as part of the solution for a free-boundary problem. A number of concrete examples illustrate the result.

Keywords: transient diffusions; last-passage times; optimal prediction; optimal stopping; free-boundary problems (search for similar items in EconPapers)
Pages: 21 pages
Date: 2014-01-01
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Citations: View citations in EconPapers (2)

Published as: Glover, K. and Hulley, H., 2014, "Optimal prediction of the last-passage time of a transient diffusion", SIAM Journal on Control and Optimization, 52(6), 3833-3853.

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