A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization

DOI10.1090/S0025-5718-04-01714-4zbMath1108.35096OpenAlexW2046955945WikidataQ115284332 ScholiaQ115284332MaRDI QIDQ4671839

Bruno Franchi, Yves Achdou, Nicoletta Tchou

Publication date: 27 April 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01714-4

zbMATH Keywords

weighted Sobolev spacesOrnstein-Uhlenbeck processregular mesh

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Degenerate parabolic equations (35K65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (4)

Variational Analysis for Options with Stochastic Volatility and Multiple Factors ⋮ Analytic approach to solve a degenerate parabolic PDE for the Heston model ⋮ Numerical methods for Lévy processes ⋮ Convergence of a class of degenerate Ginzburg-Landau functionals and regularity for a subelliptic harmonic map equation

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Balls and metrics defined by vector fields. I: Basic properties
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
• Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
• A finite element approximation for a class of degenerate elliptic equations
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach
• The Identity of Weak and Strong Extensions of Differential Operators
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