A Feynman-Kac-type formula for Lévy processes with discontinuous killing rates

DOI10.1007/s00780-016-0301-7zbMath1355.60060arXiv1502.07531OpenAlexW2471367411WikidataQ59468813 ScholiaQ59468813MaRDI QIDQ331363

Kathrin Glau

Publication date: 27 October 2016

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07531

zbMATH Keywords

Laplace transformGalerkin methodweak solutionoption pricingoccupation timevariational solutionfractional Laplace operatornonlocal operatorpartial integro-differential equationFeynman-Kac representationemployee optionkilling rateparabolic evolution equationpseudo-differential equationSobolev-Slobodeckii spacestime-inhomogeneous Lévy process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Numerical methods (including Monte Carlo methods) (91G60) Applications of stochastic analysis (to PDEs, etc.) (60H30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Financial applications of other theories (91G80) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Integro-differential operators (47G20) Pseudodifferential operators (47G30) Initial value problems for PDEs with pseudodifferential operators (35S10) Integro-partial differential equations (35R09)

Related Items (11)

Fluctuations of Omega-killed spectrally negative Lévy processes ⋮ A Flexible Galerkin Scheme for Option Pricing in Lévy Models ⋮ The inverse first passage time problem for killed Brownian motion ⋮ A finite elements approach for spread contract valuation via associated two-dimensional PIDE ⋮ Magic Points in Finance: Empirical Integration for Parametric Option Pricing ⋮ Computing credit valuation adjustment solving coupled PIDEs in the Bates model ⋮ Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models ⋮ Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations ⋮ Classification of Lévy Processes with Parabolic Kolmogorov Backward Equations ⋮ Markov-modulated affine processes ⋮ Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations

Cites Work

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• The Pricing of Options and Corporate Liabilities
• Hitchhiker's guide to the fractional Sobolev spaces
• The optimal dividend barrier in the gamma-omega model
• Occupation times of spectrally negative Lévy processes with applications
• Numerical methods for Lévy processes
• The martingale problem for a class of pseudo differential operators
• Barrier options and touch-and-out options under regular Lévy processes of exponential type
• Computational methods for quantitative finance. Finite element methods for derivative pricing
• Monte Carlo option pricing for tempered stable (CGMY) processes
• Integro-differential equations for option prices in exponential Lévy models
• Lévy matters III. Lévy-type processes: construction, approximation and sample path properties
• Approximations of small jumps of Lévy processes with a view towards simulation
• Term Structure Models Driven by General Levy Processes
• Classification of Lévy Processes with Parabolic Kolmogorov Backward Equations
• A priorierror estimates for reduced order models in finance
• An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps
• Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models
• A Reduced Basis for Option Pricing
• Reduced basis for vanilla and basket options
• Sobolev index: A classification of L\'evy processes
• Wavelet Discretizations of Parabolic Integrodifferential Equations
• Variational Solutions of the Pricing PIDEs for European Options in Lévy Models
• Financial Modelling with Jump Processes
• A Reduced Basis Method for Parametrized Variational Inequalities
• Fast deterministic pricing of options on Lévy driven assets
• Numerical solution of parabolic equations in high dimensions
• FROM RUIN TO BANKRUPTCY FOR COMPOUND POISSON SURPLUS PROCESSES
• Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance
• A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
• On Distributions of Certain Wiener Functionals

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