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Relevant bibliographies by topics / Malliavin differentiability

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Academic literature on the topic 'Malliavin differentiability'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Malliavin differentiability"

1

Mastrolia, Thibaut, Dylan Possamaï, and Anthony Réveillac. "On the Malliavin differentiability of BSDEs." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53, no. 1 (2017): 464–92. http://dx.doi.org/10.1214/15-aihp723.

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2

Balan, Raluca M., and Cheikh B. Ndongo. "Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise." International Journal of Stochastic Analysis 2017 (March 12, 2017): 1–9. http://dx.doi.org/10.1155/2017/9693153.

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We consider a stochastic partial differential equation (SPDE) driven by a Lévy white noise, with Lipschitz multiplicative term σ. We prove that, under some conditions, this equation has a unique random field solution. These conditions are verified by the stochastic heat and wave equations. We introduce the basic elements of Malliavin calculus with respect to the compensated Poisson random measure associated with the Lévy white noise. If σ is affine, we prove that the solution is Malliavin differentiable and its Malliavin derivative satisfies a stochastic integral equation.

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3

Alòs, Elisa, and Christian-Oliver Ewald. "Malliavin differentiability of the Heston volatility and applications to option pricing." Advances in Applied Probability 40, no. 01 (2008): 144–62. http://dx.doi.org/10.1017/s000186780000241x.

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We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

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Alòs, Elisa, and Christian-Oliver Ewald. "Malliavin differentiability of the Heston volatility and applications to option pricing." Advances in Applied Probability 40, no. 1 (2008): 144–62. http://dx.doi.org/10.1239/aap/1208358890.

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We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

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5

Tsumurai, Shota. "Malliavin Differentiability of CEV-Type Heston Model." Journal of Mathematical Finance 10, no. 01 (2020): 173–99. http://dx.doi.org/10.4236/jmf.2020.101012.

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6

Inahama, Yuzuru. "Malliavin differentiability of solutions of rough differential equations." Journal of Functional Analysis 267, no. 5 (2014): 1566–84. http://dx.doi.org/10.1016/j.jfa.2014.06.011.

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7

Suzuki, Ryoichi. "Malliavin differentiability of indicator functions on canonical Lévy spaces." Statistics & Probability Letters 137 (June 2018): 183–90. http://dx.doi.org/10.1016/j.spl.2018.01.024.

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8

Geiss, Christel, and Alexander Steinicke. "Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver." Stochastics 92, no. 3 (2019): 418–53. http://dx.doi.org/10.1080/17442508.2019.1626859.

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BONACCORSI, STEFANO, and MARCO FUHRMAN. "INTEGRATION BY PARTS AND SMOOTHNESS OF THE LAW FOR A CLASS OF STOCHASTIC EVOLUTION EQUATIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 01 (2004): 89–129. http://dx.doi.org/10.1142/s0219025704001475.

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We consider a Markov process X in a Hilbert space H, solution of a semilinear stochastic evolution equation driven by an infinite-dimensional Wiener process, occurring in the equation as an additive noise. Using techniques of the Malliavin calculus, under suitable assumptions, we prove an integration by parts formula for the transition probabilities νt, t>0 (the laws of Xt). We deduce results on differentiability (i.e. existence of logarithmic derivatives) of νt along a set of directions h∈H which can be described in terms of the coefficients of the equation. The general results are then ap

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10

Menoukeu-Pamen, Olivier, Thilo Meyer-Brandis, Torstein Nilssen, Frank Proske, and Tusheng Zhang. "A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s." Mathematische Annalen 357, no. 2 (2013): 761–99. http://dx.doi.org/10.1007/s00208-013-0916-3.

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Dissertations / Theses on the topic "Malliavin differentiability"

1

Yue, Wen. "Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html.

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This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic pa

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Book chapters on the topic "Malliavin differentiability"

1

Ewald, Christian-Oliver, Yajun Xiao, Yang Zou, and Tak Kuen Siu. "Malliavin differentiability of a class of Feller-diffusions with relevance in Finance." In Advances in Statistics, Probability and Actuarial Science. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814383318_0002.

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