Optimal Control in Financial Markets for the Uncertain Volatility Model

This article generalizes the well-known Black-Scholes model, specifically the uncertain volatility model. To calculate the fair price range of a payment obligation, Hamilton-Jacobi-Bellman equations are derived and transformed into nonlinear heat equations with boundary conditions. Theorems are proven stating that, for a certain class of payment obligations, solutions to nonlinear heat equations satisfy the linear heat equations. A computational example using real data is provided.