Convexity and Smoothness of Scale Functions and?de?Finetti¡¯s Control Problem
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- 作者：Andreas E. Kyprianou ; V¨ªctor Rivero and Renming Song
- 关键词：Potential analysis ; Special Bernstein function ; Scale functions for spectrally negative L¨¦vy processes ; Control theory
- 刊名：Journal of Theoretical Probability
- 出版年：2010
- 出版时间：June, 2010
- 年：2010
- 卷：23
- 期：2
- 页码：547-564
- 全文大小：455.6 KB
文摘
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.