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Convexity and smoothness of scale functions and de Finetti's control problem


Reference:

Kyprianou, A. E., Rivero, V. and Song, R. M., 2010. Convexity and smoothness of scale functions and de Finetti's control problem. Journal of Theoretical Probability, 23 (2), pp. 547-564.

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Official URL:

http://dx.doi.org/10.1007/s10959-009-0220-z

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 L,vy measure of a spectrally negative L,vy 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 L,vy 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.

Details

Item Type Articles
CreatorsKyprianou, A. E., Rivero, V. and Song, R. M.
DOI10.1007/s10959-009-0220-z
Uncontrolled Keywordscontrol theory, scale functions for spectrally negative levy processes, potential analysis, special bernstein function
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code18807

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