Tikhonov regularization for simultaneous inversion of initial value and source term of a time‐fractional Black‐Scholes equation

Abstract

This paper studies simultaneous inversion of initial value and source term of a time‐fractional Black‐Scholes equation. This problem is ill‐posed, and we use Tikhonov regularization method to solve it. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori Hölder type error estimates are derived. Finally, numerical experiments demonstrate the stability and effectiveness of the proposed regularization method.