Optimal Control in Financial Markets for the Uncertain Volatility Model
Grigory Belyavski, Natalia Danilova, Irina Zemlyakova, Gennady Ougolnitsky
Source abstract
This paper 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.
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