Volatility is a cornerstone of derivative pricing and risk assessment. Bahar Akhtari, Francesca Biagini, Andrea Mazzon, and Katharina Oberpriller extend the Feynman-Kac formula to uncertain volatility models in their paper Generalized Feynman-Kac Formula under volatility uncertainty, available on arXiv. The authors introduce a \(G\)-conditional expectation approach to solve nonlinear partial differential equations (PDEs) that arise from uncertain volatilities.

• By relaxing certain rigorous assumptions of the classical Feynman-Kac framework, this method opens doors to more general applications.
• The paper provides a viscosity solution to a nonlinear PDE by considering a \(G\)-conditional expectation of a discounted payoff.
• This technique facilitates the calculation of sublinear expectations, enhancing computational effectiveness.
• The findings have profound implications for the finance industry, particularly in options pricing and risk management.

The generalized Feynman-Kac formula under volatility uncertainty is a vital tool for finance professionals. It equips them to handle the unpredictable nature of financial markets and to devise more robust trading strategies, leading towards better risk mitigation and asset pricing strategies under uncertainty.