An ill-posed problem for the Black–Scholes equation for a profitable forecast of prices of stock options on real market data

DOI10.1088/0266-5611/32/1/015010zbMath1332.35390OpenAlexW2504058602MaRDI QIDQ2786446

Andrey V. Kuzhuget, Michael V. Klibanov, Kirill V. Golubnichiy

Publication date: 12 February 2016

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/32/1/015010

zbMATH Keywords

regularization methodill-posed problemBlack-Scholes equationinitial and boundary conditionsparabolic equation with the reversed timereal market data

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Ill-posed problems for PDEs (35R25) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items

Quasi-reversibility method and neural network machine learning for forecasting of stock option prices, Forecasting stock options prices via the solution of an ill-posed problem for the Black–Scholes equation, Determination of the initial density in nonlocal diffusion from final time measurements, Determination of the initial condition in parabolic equations from integral observations, A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance, Convexification for an inverse parabolic problem, A new Fourier truncated regularization method for semilinear backward parabolic problems, Convergent numerical methods for parabolic equations with reversed time via a new Carleman estimate

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Recovery of time dependent volatility coefficient by linearization
• Globally strictly convex cost functional for an inverse parabolic problem
• Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets
• The inverse problem of option pricing
• Global Convexity in a Three-Dimensional Inverse Acoustic Problem
• Recovering Dielectric Constants of Explosives via a Globally Strictly Convex Cost Functional