Paper Info
Title
Optimal Control With Absolutely Continuous Strategies For Spectrally Negative Levy Processes
Abstract
In the last few years there has been renewed interest in the classical control problem of de Finetti (1957) for the case where the underlying source of randomness is a spectrally negative Levy process. In particular, a significant step forward was made by Loeffen (2008), who showed that a natural and very general condition on the underlying Levy process which allows one to proceed with the analysis of the associated Hamilton-Jacobi-Bellman equation is that its Levy measure is absolutely continuous, having completely monotone density. In this paper we consider de Finetti's control problem, but with the restriction that control strategies are absolutely continuous with respect to the Lebesgue measure. This problem has been considered by Asmussen and Taksar (1997), Jeanblanc-Picque and Shiryaev (1995), and Boguslavskaya (2006) in the diffusive case, and Gerber and Shiu (2006) for the case of a Cramer-Lundberg process with exponentially distributed jumps. We show the robustness of the condition that the underlying Levy measure has a completely monotone density and establish an explicit optimal strategy for this case that envelopes the aforementioned existing results. The explicit optimal strategy in question is the so-called refraction strategy.
Year
Venue
Keywords
2012
JOURNAL OF APPLIED PROBABILITY
Scale function, ruin problem, de Finetti dividend problem, complete monotonicity
Field
DocType
Volume
Absolute continuity,Optimal control,Lebesgue measure,Robustness (computer science),Exponential distribution,Statistics,Lévy process,Mathematics,Monotone polygon,Randomness
Journal
49
Issue
ISSN
Citations 
1
0021-9002
5
PageRank 
References 
Authors
0.64
1
3
Name
Order
Citations
PageRank
Andreas E. Kyprianou1175.31
Ronnie Loeffen250.64
José Luis Pérez350.64