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We consider an inverse problem of parameter identification for a parabolic equation. The underlying practical example is the reconstruction of the unknown drift in the extended Black–Scholes option pricing model. Using a priori information about the unknown solution (i.e. its Lipschitz constant), we provide a solution to this non-linear ill-posed problem, as well as an error estimate. Other types of a priori information may be used (for example, monotonicity and/or convexity of the unknown solution).

Parameter identification problem for a parabolic equation – application to the Black–Scholes option pricing model