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

Kristoffer Glover, Hardy Hulley

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We identify the integrable stopping time τ with minimal L1-distance from the last-passage time γz associated with a given level z > 0, for an arbitrary nonnegative time-homogeneous transient diffusion X . We demonstrate that τ 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.

Original languageEnglish
Pages (from-to)3833-3853
Number of pages21
JournalSIAM Journal on Control and Optimization
Issue number6
Publication statusPublished - 2014
Externally publishedYes


  • Freeboundary problems
  • Last-passage times
  • Optimal prediction
  • Optimal stopping
  • Transient diffusions


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