Approximation of the quasi‐deviance function for the time‐changed Lévy processes by the first‐exit time of the inverse Gaussian subordinator

Stat ◽  
2021 ◽  
Author(s):  
Farouk Mselmi
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Inverse Gaussian ◽  
First Exit Time

scholarly journals Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2545-2552
Author(s):  
Farouk Mselmi
Keyword(s):  
Lévy Processes ◽  
Exponential Family ◽  
Exit Time ◽  
Levy Processes ◽  
Variance Function ◽  
Inverse Gaussian ◽  
Natural Exponential Family ◽  
First Exit Time

This paper deals with a characterization of the first-exit time of the inverse Gaussian subordinator in terms of natural exponential family. This leads us to characterize, by means its variance function, the class of L?vy processes time-changed by the first-exit time of the inverse Gaussian subordinator.

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (4) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Continuous-time methods in the study of discretely sampled functionals of Lévy processes. I. The positive process case

2007 ◽  
Vol 39 (1) ◽  
pp. 245-270 ◽  
Author(s):  
Michael Schröder
Keyword(s):  
Lévy Processes ◽  
Generalized Inverse ◽  
Moment Generating Function ◽  
Levy Processes ◽  
Asian Options ◽  
Inverse Gaussian ◽  
Contingent Claim Valuation ◽  
Reduction Series ◽  
Generalized Inverse Gaussian ◽  
The Moment

In this paper we develop a constructive approach to studying continuously and discretely sampled functionals of Lévy processes. Estimates for the rate of convergence of the discretely sampled functionals to the continuously sampled functionals are derived, reducing the study of the latter to that of the former. Laguerre reduction series for the discretely sampled functionals are developed, reducing their study to that of the moment generating function of the pertinent Lévy processes and to that of the moments of these processes in particular. The results are applied to questions of contingent claim valuation, such as the explicit valuation of Asian options, and illustrated in the case of generalized inverse Gaussian Lévy processes.

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (04) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

scholarly journals Continuous-time methods in the study of discretely sampled functionals of Lévy processes. I. The positive process case

2007 ◽  
Vol 39 (01) ◽  
pp. 245-270
Author(s):  
Michael Schröder
Keyword(s):  
Lévy Processes ◽  
Generalized Inverse ◽  
Moment Generating Function ◽  
Levy Processes ◽  
Asian Options ◽  
Inverse Gaussian ◽  
Contingent Claim Valuation ◽  
Reduction Series ◽  
Generalized Inverse Gaussian ◽  
The Moment

In this paper we develop a constructive approach to studying continuously and discretely sampled functionals of Lévy processes. Estimates for the rate of convergence of the discretely sampled functionals to the continuously sampled functionals are derived, reducing the study of the latter to that of the former. Laguerre reduction series for the discretely sampled functionals are developed, reducing their study to that of the moment generating function of the pertinent Lévy processes and to that of the moments of these processes in particular. The results are applied to questions of contingent claim valuation, such as the explicit valuation of Asian options, and illustrated in the case of generalized inverse Gaussian Lévy processes.

scholarly journals Barriers, exit time and survival probability for unimodal Lévy processes

2014 ◽  
Vol 162 (1-2) ◽  
pp. 155-198 ◽  
Author(s):  
Krzysztof Bogdan ◽  
Tomasz Grzywny ◽  
Michał Ryznar
Keyword(s):  
Survival Probability ◽  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes

scholarly journals Exit problems for general draw-down times of spectrally negative Lévy processes

2019 ◽  
Vol 56 (2) ◽  
pp. 441-457 ◽  
Author(s):  
Bo Li ◽  
Nhat Linh Vu ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Scale Functions ◽  
Dynamic Level ◽  
Running Maximum ◽  
Potential Measure ◽  
Exit Problems ◽  
Spectrally Negative Lévy Processes

AbstractFor spectrally negative Lévy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find expressions of the Laplace transforms for the two-sided exit problems involving the draw-down time. We also find the Laplace transforms for the hitting time and creeping time over the running-maximum related draw-down level, respectively, and obtain an expression for a draw-down associated potential measure. The results are expressed in terms of scale functions for the spectrally negative Lévy processes.

scholarly journals On the last exit times for spectrally negative Lévy processes

2017 ◽  
Vol 54 (2) ◽  
pp. 474-489 ◽  
Author(s):  
Yingqiu Li ◽  
Chuancun Yin ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Occupation Time ◽  
Exit Times ◽  
New Approach ◽  
Last Exit Time ◽  
Spectrally Negative Lévy Processes

Abstract Using a new approach, for spectrally negative Lévy processes we find joint Laplace transforms involving the last exit time (from a semiinfinite interval), the value of the process at the last exit time, and the associated occupation time, which generalize some previous results.

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