Regularization Method with Two Differential Operators for Simultaneous Inversion of Source Term and Initial Value in a Time-Fractional Black-Scholes Equation

This paper is devoted to identifying the source term and initial value simultaneously in a time-fractional Black-Scholes equation, which is an ill-posed problem. The inverse problem is transformed into a system of operator equations, and under certain source conditions, conditional stability is established. We propose a regularization method with two differential operators to solve the problem, error estimates by rules of a priori and a posteriori regularization parameter selection are derived, respectively. Numerical experiments are presented to validate the effectiveness of the proposed regularization method.