Abstract
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 language | English |
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Pages (from-to) | 3833-3853 |
Number of pages | 21 |
Journal | SIAM Journal on Control and Optimization |
Volume | 52 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 |
Externally published | Yes |
Keywords
- Freeboundary problems
- Last-passage times
- Optimal prediction
- Optimal stopping
- Transient diffusions