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Stochastic Analysis and Applications Volume 22, 2004 - Issue 4
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Original Articles

Martingale Representation of Functionals of Lévy Processes

Arne Løkka Department of Mathematics, University of Oslo, Blindern, Oslo, Norway; Department of Mathematics, King's College London, Room 108, Drury Lane Building, Strand, London WC2R 2LS, London, UKCorrespondence[email protected] [email protected]
Pages 867-892 | Published online: 11 Dec 2006

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Jinbiao Wu & Zaiming Liu. (2020) Optimal control of mean-field backward doubly stochastic systems driven by Itô-Lévy processes. International Journal of Control 93:4, pages 953-970.
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Giulia Di Nunno & Josep Vives. (2017) A Malliavin–Skorohod calculus in L0 and L1 for additive and Volterra-type processes. Stochastics 89:1, pages 142-170.
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Yeliz Yolcu Okur. (2012) An extension of the Clark–Ocone formula under benchmark measure for Lévy processes. Stochastics 84:2-3, pages 251-272.
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Wing Yan Yip, David A. Stephens & Sofia C. Olhede. (2010) The explicit chaotic representation of the powers of increments of Lévy processes. Stochastics 82:3, pages 257-290.
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Giulia Di Nunno, Thilo Meyer-Brandis, Bernt Øksendal & Frank Proske. (2006) Optimal portfolio for an insider in a market driven by Lévy processes§ . Quantitative Finance 6:1, pages 83-94.
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Fred Espen Benth & Arne LØkka . (2004) Anticipative calculus for Lévy processes and stochastic differential equations* . Stochastics and Stochastic Reports 76:3, pages 191-211.
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Hiroki Masuda, Lorenzo Mercuri & Yuma Uehara. (2022) Noise inference for ergodic Lévy driven SDE. Electronic Journal of Statistics 16:1.
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Minoo Bakhshmohammadlou & Rahman Farnoosh. (2021) Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus. Mathematical Sciences 15:4, pages 337-343.
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Jinbiao Wu. (2021) Stochastic viscosity solutions for stochastic integral-partial differential equations. Journal of Mathematical Physics 62:2.
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George Bouzianis, Lane P. Hughston, Sebastian Jaimungal & Leandro Sánchez-Betancourt. (2021) Lévy-Ito models in finance. Probability Surveys 18:none.
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Mateusz B. Majka. (2019) Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55:4.
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R. Farnoosh & M. Bakhshmohammadlou. (2018) A Note on the Hedging of Options by Malliavin Calculus in a Jump-Diffusion Market. Bulletin of the Iranian Mathematical Society 45:1, pages 75-88.
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Hi Jun Choe, Ji Min Lee & Jung-Kyung Lee. (2018) Malliavin calculus for subordinated Lévy process. Chaos, Solitons & Fractals 116, pages 392-401.
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Christel Geiss & Alexander Steinicke. (2016) Malliavin derivative of random functions and applications to Lévy driven BSDEs. Electronic Journal of Probability 21:none.
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Giulia Di Nunno & Erik Hove Karlsen. 2016. The Fascination of Probability, Statistics and their Applications. The Fascination of Probability, Statistics and their Applications 465 499 .
Bernt Øksendal & Agnès Sulem. (2014) Risk minimization in financial markets modeled by Itô-Lévy processes. Afrika Matematika 26:5-6, pages 939-979.
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Giulia Di Nunno & Steffen Sjursen. (2014) BSDEs driven by time-changed Lévy noises and optimal control. Stochastic Processes and their Applications 124:4, pages 1679-1709.
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Rüdiger Murr. (2013) Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures. Stochastic Processes and their Applications 123:5, pages 1729-1749.
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Sjoerd Dirksen, Jan Maas & Jan Neerven. (2013) Poisson stochastic integration in Banach spaces. Electronic Journal of Probability 18:none.
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Masafumi Hayashi & Yasushi Ishikawa. (2012) Composition with distributions of Wiener-Poisson variables and its asymptotic expansion. Mathematische Nachrichten 285:5-6, pages 619-658.
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Günter Last & Mathew D. Penrose. (2010) Poisson process Fock space representation, chaos expansion and covariance inequalities. Probability Theory and Related Fields 150:3-4, pages 663-690.
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Günter Last & Mathew D. Penrose. (2011) Martingale representation for Poisson processes with applications to minimal variance hedging. Stochastic Processes and their Applications 121:7, pages 1588-1606.
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S. Peszat. (2011) Lévy–Ornstein–Uhlenbeck transition semigroup as second quantized operator. Journal of Functional Analysis 260:12, pages 3457-3473.
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Wing Yan Yip, David Stephens & Sofia Olhede. (2010) HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET. Mathematical Finance 20:4, pages 617-646.
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Jin Ma. 2010. Encyclopedia of Quantitative Finance. Encyclopedia of Quantitative Finance.
Xicheng Zhang. (2009) Clark–Ocone formula and variational representation for Poisson functionals. The Annals of Probability 37:2.
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Stefan Ankirchner. (2008) On filtration enlargements and purely discontinuous martingales. Stochastic Processes and their Applications 118:9, pages 1662-1678.
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Elisa Alòs, Jorge A. León, Monique Pontier & Josep Vives. (2008) A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility. Journal of Applied Mathematics and Stochastic Analysis 2008, pages 1-17.
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Constantin Tudor. (2007) An anticipating calculus for square integrable pure jump Levy processes. Random Operators and Stochastic Equations 15:1, pages 1-14.
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Zhiyuan Huang & Ying Wu. (2005) Lévy White Noise Calculus Based on Interaction Exponents. Acta Applicandae Mathematicae 88:3, pages 251-268.
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Florian Huehne. (2005) Malliavin Calculus for the Computation of Greeks in Markets Driven by Pure-Jump Levy Processes. SSRN Electronic Journal.
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Yajun Xiao. (2009) R-Minimizing Hedging in an Incomplete Market: Malliavin Calculus Approach. SSRN Electronic Journal.
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Wing Yan Yip, David A. Stephens & Sofia C. Olhede. (2008) Hedging Strategies and Minimal Variance Portfolios for European and Exotic Options in a Levy Market. SSRN Electronic Journal.
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Elisa Alos, Jorge A. Leon, Monique Pontier & Josep Vives. (2008) A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility. SSRN Electronic Journal.
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