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

Andreas E. Kyprianou, Víctor Rivero, Renming Song

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)547-564
Number of pages18
JournalJournal of Theoretical Probability
Issue number2
StatePublished - Jun 2010


  • Control theory
  • Potential analysis
  • Scale functions for spectrally negative Lévy processes
  • Special Bernstein function

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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