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

Publication Type:
Journal Article
SIAM Journal on Control and Optimization, 2014, 52 (6), pp. 3833 - 3853
Issue Date:
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© 2014 Society for Industrial and Applied Mathematics 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.
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