scholarly journals Occupation time of Lévy processes with jumps rational Laplace transforms

2018 ◽  
Vol 23 ◽  
Author(s):  
Ait-Aoudia Djilali
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Occupation Time

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.

scholarly journals A Subordination Principle on Wright Functions and Regularized Resolvent Families

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Luciano Abadias ◽  
Pedro J. Miana
Keyword(s):  
Fractional Calculus ◽  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Cauchy Problems ◽  
Convolution Properties ◽  
Vector Valued ◽  
Resolvent Families

We obtain a vector-valued subordination principle forgα,gβ-regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.

Occupation times of Lévy processes

2021 ◽  
pp. 2142003
Author(s):  
Lan Wu ◽  
Xiao Zhang
Keyword(s):  
Explicit Formula ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Occupation Time ◽  
Applied Probability ◽  
Occupation Times ◽  
Financial Applications ◽  
Pricing Problems

In this paper, we give a complete and succinct proof that an explicit formula for the occupation time holds for all Lévy processes, which is important to the pricing problems of various occupation-time-related derivatives such as step options and corridor options. We construct a sequence of Lévy processes converging to a given Lévy process to obtain our conclusion. Besides financial applications, the mathematical results about occupation times of a Lévy process are of interest in applied probability.

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.

On correlating Lévy processes

2010 ◽  
Vol 13 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Ernst Eberlein ◽  
Dilip Madan
Keyword(s):  
Lévy Processes ◽  
Levy Processes
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