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Convexity and Smoothness of Scale Functions and de Finetti´s Control Problem | |
VICTOR MANUEL RIVERO MERCADO | |
Acceso Abierto | |
Atribución-NoComercial | |
Procesos de Levy | |
Motivated by a classical control problem from actuarial mathematics, we study smoothness and convexity properties of q -scale functions for spectrally negative Levy processes. Continuing from the very recent work of [2] and [24] we strengthen their collective conclusions by showing, amongst other results, that whenever the Levy mea- sure has a non-increasing density which is log convex then for q > 0 the scale function W ( q ) is convex on some half line ( a ; 1 ) where a is the largest value at which W ( q ) 0 attains its global minimum. As a consequence we deduce that de Finetti's classical actuarial control problem is solved by a barrier strategy where the barrier is positioned at height. | |
Centro de Investigación en Matemáticas AC | |
24-01-2008 | |
Reporte | |
Inglés | |
Investigadores | |
PROCESOS DE MARKOV | |
Versión publicada | |
publishedVersion - Versión publicada | |
Appears in Collections: | Reportes Técnicos - Probabilidad y Estadística |
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