Last Exit Before an Exponential Time for Spectrally Negative Lévy Processes
نویسندگان
چکیده
منابع مشابه
Last Exit before an Exponential Time for Spectrally Negative Lévy Processes
Chiu and Yin (2005) found the Laplace transform of the last time a spectrally negative Lévy process, which drifts to∞, is below some level. The main motivation for the study of this random time stems from risk theory: what is the last time the risk process, modeled by a spectrally negative Lévy process drifting to ∞, is 0? In this paper we extend the result of Chiu and Yin, and we derive the La...
متن کاملOptimal portfolios for exponential Lévy processes
We consider the problem of maximizing the expected utility from consumption or terminal wealth in a market where logarithmic securities prices follow a Lévy process. More specifically, we give explicit solutions for power, logarithmic and exponential utility in terms of the Lévy-Chinchine triplet. In the first two cases, a constant fraction of current wealth should be invested in each of the se...
متن کاملA martingale review of some fluctuation theory for spectrally negative Lévy processes ∗
We give a review of elementary fluctuation theory for spectrally negative Lévy processes using for the most part martingale theory. The methodology is based on techniques found in Kyprianou and Palmowski (2003) which deals with similar issues for a general class of Markov additive processes.
متن کاملOptimal Control with Absolutely Continuous Strategies for Spectrally Negative Lévy Processes
In the last few years there has been renewed interest in the classical control problem of de Finetti [10] for the case that underlying source of randomness is a spectrally negative Lévy process. In particular a significant step forward is made in [25] where it is shown that a natural and very general condition on the underlying Lévy process which allows one to proceed with the analysis of the a...
متن کاملPhase-type fitting of scale functions for spectrally negative Lévy processes
We study the scale function of the spectrally negative phase-type Lévy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phase-type distributions is dense in the class of all positive-valued distributions, we propose a new approach to approximating the scale function and the associated fluctuatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2009
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1245676105