By Violetta Bernyk and others

Given a stable L\'{e}vy process *X=(X_t)_{0\le t\le T}* of index *\alpha\in(1,2)* with no negative jumps, and letting *S_t=\sup_{0\le s\le t}X_s* denote its running supremum for *t\in [0,T]*, we consider the optimal prediction problem \[V=\inf_{0\le\tau\le T}\mathsf{E}(S_T-X_{\tau})^p,\] where the infimum is taken over all stopping times *\tau* of *X*, and the error... Show more

February 9, 2012

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Predicting the ultimate supremum of a stable Lévy process with no negative jumps

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