The Domain of Partial Attraction of an Infinitely Divisible Law Without a Normal Component

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.

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Learning for infinitely divisible GARCH models in option pricing

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2019-0088 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Fumin Zhu ◽

Michele Leonardo Bianchi ◽

Young Shin Kim ◽

Frank J. Fabozzi ◽

Hengyu Wu

Keyword(s):

Option Pricing ◽

Stock Returns ◽

Bayesian Learning ◽

Space Structure ◽

Estimation Methods ◽

Garch Models ◽

Learning Approaches ◽

Infinitely Divisible ◽

Asymmetric Garch ◽

Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

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The I-Love-Q Relations for Superfluid Neutron Stars

Universe ◽

10.3390/universe7040111 ◽

2021 ◽

Vol 7 (4) ◽

pp. 111

Author(s):

Cheung-Hei Yeung ◽

Lap-Ming Lin ◽

Nils Andersson ◽

Greg Comer

Keyword(s):

Fluid Dynamics ◽

Equation Of State ◽

Neutron Stars ◽

Quadrupole Moment ◽

Fluid Model ◽

Normal Component ◽

Approximate Equation ◽

Mean Field Model ◽

Polytropic Model ◽

Two Fluid

The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio Ωn/Ωp between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating Ωn/Ωp≈1. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as O(10%) if Ωn/Ωp differ from unity by a few tens of percent. As Ωn/Ωp≈1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability.

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