Martingale Representation of Functionals of Lévy Processes

DOI10.1081/SAP-120037622zbMath1060.60058OpenAlexW2009805587MaRDI QIDQ4826122

Arne Løkka

Publication date: 11 November 2004

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/sap-120037622

zbMATH Keywords

Lévy processeshedgingMalliavin calculusPoisson random measuremartingale representation

Mathematics Subject Classification ID

Related Items (24)

Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus ⋮ Composition with distributions of Wiener-Poisson variables and its asymptotic expansion ⋮ HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET ⋮ Noise inference for ergodic Lévy driven SDE ⋮ Hedging Under Worst-Case-Scenario in a Market Driven by Time-Changed Lévy Noises ⋮ Malliavin calculus for subordinated Lévy process ⋮ BSDEs driven by time-changed Lévy noises and optimal control ⋮ A note on the hedging of options by Malliavin calculus in a jump-diffusion market ⋮ Risk minimization in financial markets modeled by Itô-Lévy processes ⋮ On filtration enlargements and purely discontinuous martingales ⋮ An extension of the Clark–Ocone formula under benchmark measure for Lévy processes ⋮ Lévy-Ornstein-Uhlenbeck transition semigroup as second quantized operator ⋮ The explicit chaotic representation of the powers of increments of Lévy processes ⋮ Martingale representation for Poisson processes with applications to minimal variance hedging ⋮ An anticipating calculus for square integrable pure jump Levy processes ⋮ Poisson process Fock space representation, chaos expansion and covariance inequalities ⋮ Lévy-Ito models in finance ⋮ Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling ⋮ 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 ⋮ Optimal control of mean-field backward doubly stochastic systems driven by Itô-Lévy processes ⋮ Clark-Ocone formula and variational representation for Poisson functionals ⋮ Optimal portfolio for an insider in a market driven by Lévy processes§ ⋮ Stochastic viscosity solutions for stochastic integral-partial differential equations ⋮ Lévy white noise calculus based on interaction exponents

Cites Work

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• Option hedging for semimartingales
• Anticipating integrals for a class of martingales
• Anticipative Markovian transformations on the Poisson space.
• On Lévy processes, Malliavin calculus and market models with jumps
• Chaotic and predictable representations for Lévy processes.
• On the existence of smooth densities for jump processes
• Spectral Type of the Shift Transformation of Differential Processes With Stationary Increments
• The normal inverse gaussian lévy process: simulation and approximation
• Chaotic and variational calculus in discrete and continuous time for the poisson process
• White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance

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