Asymmetric skew Bessel processes and their applications to finance

Decamps, Marc; Goovaerts, Marc; Schoutens, Wim

doi:10.1016/j.cam.2005.03.067

Cited by 30 publications

(26 citation statements)

References 11 publications

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“…Skew Brownian motion has more recently emerged in connection with diverse applications ranging from a variant on the multi-arm bandit problem [Barlow et al (2000)], mathematical finance [Decamps, Goovaerts and Schoutens (2006)], Monte-Carlo simulation schemes [Lejay and Martinez (2006)] and dispersion in heterogeneous media [Freidlin and Sheu (2000), Ramirez et al (2006Ramirez et al ( , 2008]. The present paper provides new theoretical results for functionals of skew Brownian motion and its associated semi-group theory (p.d.e.…”

Section: Introduction Skew Brownian Motion Was Introduced Bymentioning

confidence: 86%

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

Appuhamillage¹,

Bokil²,

Thomann³

et al. 2011

Ann. Appl. Probab.

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Section: Introduction Skew Brownian Motion Was Introduced Bymentioning

confidence: 86%

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

Appuhamillage¹,

Bokil²,

Thomann³

et al. 2011

Ann. Appl. Probab.

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“…They are not hard to derive directly, but the reader may see, e.g., [9,10,4,16] and the references therein for more details and many additional results. The Lévy skew stable probability distribution is the Fourier transform of its characteristic function φ, defined as follows.…”

Section: Lévy Skew Stable Processesmentioning

confidence: 99%

Exploration trees and conformal loop ensembles

2009

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We construct and study the conformal loop ensembles CLE(κ), defined for 8/3 ≤ κ ≤ 8, using branching variants of SLE(κ) called exploration trees. The CLE(κ) are random collections of countably many loops in a planar domain that are characterized by certain conformal invariance and Markov properties. We conjecture that they are the scaling limits of various random loop models from statistical physics, including the O(n) loop models.

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“…Processes of the studied type and their square roots can be well applied in financial mathematics (see e.g. [8], [9], and below). Therefore, the tractability of such processes is an important issue.…”

Section: Motivationsmentioning

confidence: 99%

Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

Trutnau

2011

Stochastic Processes and their Applications

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Let σ, δ > 0, b ≥ 0. Let λ 2 : R + → R + , be continuous, and locally of bounded variation. We develop a general analytic criterion for the pathwise uniqueness ofwhere p ∈ (0, 1), and ℓ 0 t (R−λ 2 ) is the symmetric semimartingale local time of R−λ 2 . The criterion is related to the existence of nice (Kummer) functions for the time dependent infinitesimal generator of R. As a corollary we obtain explicit sufficient conditions for pathwise uniqueness. These are expressed in terms of λ 2 , its derivative, and the parameters σ, δ, b, p.2000 Mathematics Subject Classification: Primary: 60H10, 60J60, 60J55; Secondary: 35K20.

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Asymmetric skew Bessel processes and their applications to finance

Cited by 30 publications

References 11 publications

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

Exploration trees and conformal loop ensembles

Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

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