A DIRECT SOLUTION TO THE FOKKER–PLANCK EQUATION FOR EXPONENTIAL BROWNIAN FUNCTIONALS

DOI10.1142/S0219530510001655zbMath1206.60061MaRDI QIDQ3580191

Caroline Pintoux, Nicolas Privault

Publication date: 11 August 2010

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

zbMATH Keywords

Fokker-Planck equationspectral expansionBessel functionDothan modelBrownian exponential functional

Mathematics Subject Classification ID

Brownian motion (60J65) Microeconomic theory (price theory and economic markets) (91B24) Applications of stochastic analysis (to PDEs, etc.) (60H30) Analyticity in context of PDEs (35A20) Path integrals in quantum mechanics (81S40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (8)

The \(\alpha\)-hypergeometric stochastic volatility model ⋮ Monte Carlo computation of the Laplace transform of exponential Brownian functionals ⋮ Finite-Time Blowup and Existence of Global Positive Solutions of a Semi-linear Stochastic Partial Differential Equation with Fractional Noise ⋮ Finite-time blow-up of a non-local stochastic parabolic problem ⋮ Exponential Functionals of Brownian Motion and Explosion Times of a System of Semilinear SPDEs ⋮ Global and non-global solutions of a fractional reaction-diffusion equation perturbed by a fractional noise ⋮ THE DOTHAN PRICING MODEL REVISITED ⋮ Kolmogorov distance between the exponential functionals of fractional Brownian motion

Cites Work

• Unnamed Item
• Unnamed Item
• Exponential functionals of Brownian motion. I: Probability laws at fixed time
• Laguerre Series for Asian and Other Options
• On some exponential functionals of Brownian motion
• Diffusion in a one-dimensional random medium and hyperbolic Brownian motion
• A study of the Hartman–Watson distribution motivated by numerical problems related to the pricing of Asian options
• Bessel Processes, the Integral of Geometric Brownian Motion, and Asian Options
• Spectral Expansions for Asian (Average Price) Options

This page was built for publication: A DIRECT SOLUTION TO THE FOKKER–PLANCK EQUATION FOR EXPONENTIAL BROWNIAN FUNCTIONALS