Abstract

The core of my talk is devoted to explain rough stochastic differential equations (RSDEs), a common generalization of Ito SDEs and Lyons RDEs. With concrete motivation from (I) non-linear filtering theory, (II) pathwise stochastic control and (III) a recent rough PDE approach to pricing in non-Markovian stochastic volatility models, I will then indicate all the progress made possible with RSDEs. The talk is based on Friz, P. K., Lê, K., Hocquet, A. (2021-2024). Rough stochastic differential equations. https://arxiv.org/abs/2106.10340Friz, P. K., Lê, K., Zhang, H. (2024). Controlled rough SDEs, pathwise stochastic control and dynamic programming principles. https://arxiv.org/abs/2412.05698.Bugini, F., Friz, P. K., Zhang, H., Lê, K. (2025). Rough path stability of the filtering problem, revisited. Work in preparation.Bank, P., Bayer, C., Friz, P. K., Pelizzari, L. (2025). Rough PDEs for local stochastic volatility models. To appear in Math. Finance and https://arxiv.org/abs/2307.09216