Bernyk, ViolettaDalang, Robert C.Peskir, Goran2012-06-122012-06-122012-06-12201110.1214/10-AOP598https://infoscience.epfl.ch/handle/20.500.14299/81605WOS:000297849900008Given a stable Levy process X = (X-t)(0 <= t <= T) of index alpha is an element of (1, 2) with no negative jumps, and letting S-t = sup(0 <= s <= t) X-s denote its running supremum for t is an element of [0, T], we consider the optimal prediction problemOptimal predictionoptimal stoppingultimate supremumstable Levy process with no negative jumpsspectrally positivefractional free-boundary problemRiemann-Liouville fractional derivativeCaputo fractional derivativestochastic process reflected at its supremuminfinitesimal generatorweakly singular Volterra integral equationpolar kernelsmooth fitcurved boundaryBrownian-MotionMaximumtext::journal::journal article::research article