| Abstract: |
| In this talk, we present modeling of financial dynamics under uncertainty through stochastic volatility frameworks. We introduce several stochastic models, with a particular focus on an $\alpha$-hypergeometric model with uncertain volatility (UV), and investigate the corresponding worst-case scenario for option pricing. Our approach relies on the connection between a class of nonlinear Hamilton-Jacobi-Bellman (HJB) type partial differential equations, namely G-HJB equations, which characterize the nonlinear expectation in the UV setting and second-order backward stochastic differential equations (2BSDEs). This framework provides an alternative to the challenging calibration issues inherent in uncertain volatility models. Using asymptotic analysis of the G-HJB equation and its equivalent 2BSDE representation, we derive a limiting model that accurately captures the worst-case pricing scenario when the volatility bounds vary slowly. Finally, the theoretical results are supported by numerical experiments based on deep learning methods for approximating the associated 2BSDE, demonstrating the effectiveness of the proposed approach. |
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