scholarly journals Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Krzysztof Bisewski ◽  
Jevgenijs Ivanovs
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Process Failure ◽  
Dense Grid ◽  
Threshold Exceedance

scholarly journals LAN property for a simple Lévy process

2014 ◽  
Vol 352 (10) ◽  
pp. 859-864 ◽  
Author(s):  
Arturo Kohatsu-Higa ◽  
Eulalia Nualart ◽  
Ngoc Khue Tran
Keyword(s):  
Lévy Process ◽  
Levy Process

scholarly journals On the optimal dividend problem for a spectrally negative Lévy process

2007 ◽  
Vol 17 (1) ◽  
pp. 156-180 ◽  
Author(s):  
Florin Avram ◽  
Zbigniew Palmowski ◽  
Martijn R. Pistorius
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Spectrally Negative Lévy Process ◽  
Optimal Dividend

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

scholarly journals Last Exit Before an Exponential Time for Spectrally Negative Lévy Processes

2009 ◽  
Vol 46 (02) ◽  
pp. 542-558 ◽  
Author(s):  
E. J. Baurdoux
Keyword(s):  
Laplace Transform ◽  
Lévy Process ◽  
Risk Process ◽  
Levy Process ◽  
Risk Theory ◽  
Exponential Time ◽  
Main Motivation ◽  
Spectrally Negative Lévy Process ◽  
The Laplace Transform ◽  
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 Laplace transform of the last time, before an independent, exponentially distributed time, that a spectrally negative Lévy process (without any further conditions) exceeds (upwards or downwards) or hits a certain level. As an application, we extend a result found in Doney (1991).

scholarly journals A factorization of a Lévy process over a phase-type horizon

2018 ◽  
Vol 34 (4) ◽  
pp. 397-408 ◽  
Author(s):  
Søren Asmussen ◽  
Jevgenijs Ivanovs
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Phase Type
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