Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem

Andreas E. Kyprianou (), Víctor Rivero () and Renming Song ()
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Andreas E. Kyprianou: University of Bath
Víctor Rivero: University of Bath
Renming Song: University of Illinois

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 547-564

Abstract: Abstract We continue the recent work of Avram et al. (Ann. Appl. Probab. 17:156–180, 2007) and Loeffen (Ann. Appl. Probab., 2007) by showing that whenever the Lévy measure of a spectrally negative Lévy process has a density which is log-convex then the solution of the associated actuarial control problem of de Finetti is solved by a barrier strategy. Moreover, the level of the barrier can be identified in terms of the scale function of the underlying Lévy process. Our method appeals directly to very recent developments in the theory of potential analysis of subordinators and their application to convexity and smoothness properties of the relevant scale functions.

Keywords: Potential analysis; Special Bernstein function; Scale functions for spectrally negative Lévy processes; Control theory; 60J99; 93E20; 60G51 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-009-0220-z

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