Convergence of Inverse Volatility Problem Based on Degenerate Parabolic Equation

Based on the theoretical framework of Black–Scholes model, convergence inverse volatility problem based degenerate parabolic equation is studied. Being different from other problems in classical equations, we introduce some variable substitutions to convert original into an principal coefficient a bounded area, which unknown can be recovered and deficiencies caused by artificial truncation solved. optimal control framework, transformed optimization existence minimizer established, rigorous mathematical proof given for solution. In end, gradient-type iteration method applied obtain numerical solution problem, experiments are performed.