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

Andreas E Kyprianou, Victor Rivero, R M Song

Research output: Contribution to journalArticle

22 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)547-564
Number of pages18
JournalJournal of Theoretical Probability
Volume23
Issue number2
DOIs
Publication statusPublished - Jun 2010

Keywords

  • control theory
  • scale functions for spectrally negative Levy processes
  • potential analysis
  • special Bernstein function

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