منابع مشابه
Option pricing with log-stable Lévy processes
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix E onto a non-random vector. The scaling index E models prices of the individual financial assets (stocks, mutual funds, etc.). We find the functional form of the characteristic function of real powers of the price returns a...
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Let {Rt, 0 ≤ t ≤ 1} be a symmetric α-stable Riemann-Liouville process with Hurst parameterH > 0. Consider a translation invariant, β-self-similar, and p-pseudo-additive functional semi-norm ||.||. We show that if H > β+1/p and γ = (H − β− 1/p), then lim ε↓0 ε logP [||R|| ≤ ε] = −K ∈ [−∞, 0), with K finite in the Gaussian case α = 2. If α < 2, we prove that K is finite when R is continuous and H...
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The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the f...
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We are interested in the differential equations satisfied by the density of the Geometric Stable processes { G α(t); t ≥ 0 } , with stability index α ∈ (0, 2] and symmetry parameter β ∈ [−1, 1], both in the univariate and in the multivariate cases. We resort to their representation as compositions of stable processes with an independent Gamma subordinator. As a preliminary result, we prove that...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1988
ISSN: 0304-4149
DOI: 10.1016/0304-4149(88)90093-2