The Source Term Inversion of a Time‐Fractional Black‐Scholes Equation by Fractional Landweber Iterative Regularization Method

ABSTRACT This paper studies the source term inversion of a time‐fractional Black‐Scholes equation, which is an ill‐posed problem. Under certain assumptions, we establish conditional stability results and derive the optimal error bound for the problem. The fractional Landweber iterative regularization method is employed to tackle this problem. Based on the selection rules of a priori and a posteriori regularization parameters, the optimal error estimates of regularization solutions are presented. Numerical examples demonstrate that the proposed regularization method is both effective and stable.