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Lévy processes and infinitely divisible distributions
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In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.Abstract:
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.read more
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BookDOI
Fluctuations of Lévy Processes with Applications
TL;DR: In this article, Kloeden, P., Ombach, J., Cyganowski, S., Kostrikin, A. J., Reddy, J.A., Pokrovskii, A., Shafarevich, I.A.
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Ten equivalent definitions of the fractional laplace operator
TL;DR: In this article, several definitions of the Riesz fractional Laplace operator in R^d have been studied, including singular integrals, semigroups of operators, Bochner's subordination, and harmonic extensions.
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Optimal stopping and perpetual options for Lévy processes
TL;DR: A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained.
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Density and tails of unimodal convolution semigroups
TL;DR: For the isotropic unimodal probability convolutional semigroups, this article gave sharp bounds for their Levy-Khintchine exponent with Matuszewska indices strictly between 0 and 2.
Extreme Events: Dynamics, Statistics and Prediction
TL;DR: In this paper, the authors review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics.
References
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Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape.
Kamil Kaleta,József Lőrinczi +1 more
TL;DR: A new phenomenon which manifests as a qualitative transition in the spatial decay behavior of the stationary measure of a jump process under an external potential is reported, occurring on a combined change in the characteristics of the process and the lowest eigenvalue resulting from the effect of the potential.
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The Lucas Orchard
TL;DR: In this article, the authors investigate the behavior of asset prices in an endowment economy in which a representative agent with power utility consumes the dividends of multiple assets The assets are Lucas trees; a collection of Lucas trees is a Lucas orchard The model generates return correlations that vary endogenously, spiking at times of disaster.
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Nonparametric adaptive estimation of linear functionals for low frequency observed L evy processes
TL;DR: In this paper, the authors construct kernel estimators for linear functionals of and provide rates of convergence under regularity assumptions, and consider adaptive estimation via model selection and propose a new strategy for the data driven choice of the smoothing parameter.
Journal ArticleDOI
On a Heath–Jarrow–Morton approach for stock options
Jan Kallsen,Paul Krühner +1 more
TL;DR: In this article, the authors transfer the Heath-Jarrow-Morton approach to the modelling of call options with all strikes and maturities, and provide necessary and sufficient conditions for absence of arbitrage.
Journal ArticleDOI
On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
TL;DR: In this article, a continuous-time dynamic spectral risk measure (DSR) is proposed, which is defined in terms of certain backward stochastic differential equations, and shown to arise in the limit of a sequence of such iterated spectral risk measures driven by lattice random walks, under suitable scaling and vanishing temporal and spatial mesh sizes.