Bismut-Elworthy-Li-type formulae for stochastic differential equations with jumps

DOI10.1007/s10959-010-0280-0zbMath1202.60092arXiv1002.1384OpenAlexW2039754057MaRDI QIDQ975336

Atsushi Takeuchi

Publication date: 9 June 2010

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1384

zbMATH Keywords

Malliavin calculusHeat kernelJump processLogarithmic derivative

Mathematics Subject Classification ID

Related Items (20)

Regularity for distribution-dependent SDEs driven by jump processes ⋮ Bismut formula for Lions derivative of distribution-path dependent SDEs ⋮ On Malliavin's proof of Hörmander's theorem ⋮ Exponential ergodicity and regularity for equations with Lévy noise ⋮ Integration by parts formulas for marked Hawkes processes ⋮ Derivative formula and exponential convergence for semilinear SPDEs driven by Lévy processes ⋮ Computation of Greeks for asset price dynamics driven by stable and tempered stable processes ⋮ Gradient formulas for jump processes on manifolds ⋮ Computing deltas without derivatives ⋮ Derivative formulae for stochastic differential equations driven by Poisson random measures ⋮ Derivative formulae for SDEs driven by multiplicative \(\alpha\)-stable-like processes ⋮ Derivative Formula and Harnack Inequality for SDEs Driven by Lévy Processes ⋮ Gradient estimates and coupling property for semilinear SDEs driven by jump processes ⋮ Irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise ⋮ Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise ⋮ Strong Feller property for SDEs driven by multiplicative cylindrical stable noise ⋮ Derivative formula and coupling property for linear SDEs driven by Lévy processes ⋮ Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling ⋮ GREEKS FORMULAS FOR AN ASSET PRICE MODEL WITH GAMMA PROCESSES ⋮ Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent Lévy processes

Cites Work

• Large deviations and the Malliavin calculus
• Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps
• Sensitivity analysis for averaged asset price dynamics with gamma processes
• Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group
• Formulae for the derivatives of heat semigroups
• Computations of Greeks in a market with jumps via the Malliavin calculus
• On the existence of smooth densities for jump processes
• Applications of Malliavin calculus to Monte Carlo methods in finance
• Integration by parts formula for locally smooth laws and applications to sensitivity computations
• Malliavin Monte Carlo Greeks for jump diffusions
• The Malliavin Calculus and Related Topics
• Calcul des variations stochastique et processus de sauts
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