Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes [PDF]
, 2016 In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unimodal Levy processes.
T. Grzywny, Mateusz Kwaśnicki
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Application of Lévy processes in modelling (geodetic) time series with mixed spectra [PDF]
Nonlinear Processes in Geophysics, 2021 Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series together with the estimated geophysical signals.
J.-P. Montillet +5 more
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Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes
, 2017 In this paper, we investigate an optimal periodic dividend and capital injection problem for spectrally positive Levy processes. We assume that the periodic dividend strategy has exponential inter-dividend-decision times and continuous monitoring of ...
Yongxia Zhao, Ping Chen, Hailiang Yang
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BSDEs and log-utility maximization for Lévy processes
Modern Stochastics: Theory and Applications, 2019 In this paper we establish the existence and the uniqueness of the solution of a special class of BSDEs for Lévy processes in the case of a Lipschitz generator of sublinear growth.
Paolo Di Tella, Hans-Jürgen Engelbert
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Asymptotic results for exponential functionals of Levy processes [PDF]
, 2016 In this work we give a complete description to the asymptotic behaviors of exponential functionals of L\'evy processes and divide them into five different types according to their convergence rates. Not only their exact convergence speeds are proved, the
Zenghu Li, Wei Xu
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Fluctuations of Omega-killed spectrally negative Lévy processes [PDF]
Stochastic Processes and their Applications, 2016 In this paper we solve the exit problems for a (reflected) spectrally negative L\'evy process exponentially killed with killing intensity depending on the present state of the process. We analyze respective resolvents.
Bo-Yan Li, Z. Palmowski
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Barrier Option Under Lévy Model : A PIDE and Mellin Transform Approach
Mathematics, 2016 We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform.
Sudip Ratan Chandra, Diganta Mukherjee
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Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes
Journal of Mathematics, 2023 In this paper, a new approach is proposed to construct willow tree (WT) for generalized hyperbolic (GH) Lévy processes. There are two advantages of our proposed approach compared to the classical WT methods.
Hongying Wu, Zhiqiang Zhou, Caijuan Kang
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Jumping to Conclusion? A Lévy Flight Model of Decision Making [PDF]
Tutorials in Quantitative Methods for Psychology, 2020 The diffusion model is one of the most prominent response time models in cognitive psychology. The model describes evidence accumulation as a stochastic process that runs between two boundaries until a threshold is hit, and a decision is made.
Wieschen, Eva Marie +2 more
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On Approximation of Some Lévy Processes
Austrian Journal of StatisticsIn this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting ...
Dmytro Ivanenko +2 more
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