Fluctuation theory for level-dependent Lévy risk processes
نویسندگان
چکیده
منابع مشابه
A 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 کاملRisk bounds of learning processes for Lévy processes
Lévy processes refer to a class of stochastic processes, for example, Poisson processes and Brownian motions, and play an important role in stochastic processes and machine learning. Therefore, it is essential to study risk bounds of the learning process for time-dependent samples drawn from a Lévy process (or briefly called learning process for Lévy process). It is noteworthy that samples in t...
متن کاملRuin Probabilities and Overshoots for General Lévy Insurance Risk Processes
We formulate the insurance risk process in a general Lévy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to −∞ a.s. and the positive tail of the Lévy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asm...
متن کاملStochastic Bounds for Lévy Processes
Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrat...
متن کاملLévy Processes in Finance : Theory , Numerics , and Empirical Facts
Preface Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible distribution can be chosen as the increment distribution over periods of time ∆t. On the other hand, they have a simple structure in comparison with general semimartingales. Thus stochastic models ba...
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: Stochastic Processes and their Applications
سال: 2019
ISSN: 0304-4149
DOI: 10.1016/j.spa.2019.03.006