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Fwd: International Seminar on SDEs and Related Topics: Rainer Buckdahn June 06
by Gianmario Tessitore - UNIMIB 02 Jun '25

02 Jun '25

Diffondo volentieri Mario ---------- Forwarded message --------- Da: Stefan Geiss <geiss(a)jyu.fi> Date: lun 2 giu 2025 alle ore 07:58 Subject: Fwd: International Seminar on SDEs and Related Topics: Rainer Buckdahn June 06 To: <gianmario.tessitore(a)unimib.it> Dear Mario, we got the info for next week's talk. Best wishes Stefan ------------------------------------------------ Friday, June 06, (12:30 noon London, 1:30 pm Berlin, 2:30 pm Helsinki, 7:30 pm Beijing) in the *International Seminar on SDEs and Related Topics* in Zoom https://jyufi.zoom.us/j/61891007917 *Rainer Buckdahn* (Université de Bretagne Occidentale, Brest, France, Shandong University Qingdao, China) will speak about *Optimal control problems with generalized mean-field dynamics* *and viscosity solutions to a Master Bellman equation* Abstract: We study an optimal control problem with generalized mean-field dynamics with open-loop controls, where the coefficients depend not only on the state processes and controls, but also on the joint law of them. The value function V which is defined in a classical way, does not satisfy the Dynamic Programming Principle (DPP for short). Indeed, we show that V solely satisfies the one-sided DPP. For this reason we introduce subtly a novel value function ϑ, which is closely related to the original value function V, so that a characterisation of ϑ as a solution of a partial differential equation (PDE) also characterises V. We establish the DPP for ϑ. By using an intrinsic notion of viscosity solution, initially introduced in Burzoni, Ignazio, Reppen and Soner and specifically tailored to our framework, we show that the value function ϑ is a viscosity solution to a Master Bellman equation on a subset of the Wasserstein space of probability measures with second order moment. The uniqueness of the viscosity solution is proved for coefficients which depend on the time and the joint law of the control process and the controlled process. The talk is based on joint work with Juan Li (SDU, Qingdao and Weihai) and Zhanxin Li (SDU, Weihai). ==== about the speaker ==== Rainer Buckdahn studied Mathematics at the Friedrich Schiller University Jena (Germany) and obtained his doctoral degree, directed by H.-J. Engelbert, in 1985. After that he held a position at the Humboldt University Berlin and completed his habilitation in 1992. In 1994 he became a professor at the University of Western Brittany (Brest, France). Rainer Buckdahn is a leading specialist in stochastic process theory with an emphasis on stochastic control and differential games, stochastic differential equations, various types of backward stochastic differential equations, and stochastic partial differential equations. Rainer Buckdahn was awarded a fellowship by the French Ministry of Research and Technology and a Heisenberg grant by the German "Deutsche Forschungsgesellschaft". He is also a member of the Academic Faculty of the "Research Centre for Mathematics and Interdisciplinary Sciences Centre" at Shandong University (China). Finally, he acts as executive editor of the journal "Probability, Uncertainty and Quantitative Risk". -- Gianmario Tessitore Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca

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