Welcome to a webinar in stochastic analysis, statistics and machine learning, arranged within the research field Deterministic and Stochastic Modelling.
On conditional McKean-Vlasov SDEs and relate problems
Professor Jin Ma, director, Mathematical Finance Program, Dana and David Dornsife College of Letters, Arts & Sciences, Department of Mathematics,
University of Southern California, USA
We study a class of conditional McKean-Vlasov SDEs (CMVS-DEs, for short), in which all dynamics involve both the state and the conditional law of the solution, given the information via an observation equation. Due to the lack of continuous dependence of the conditional laws with respect to the underlying state-observation processes, the usual iteration scheme encounters some fundamental diffculties in producing the desired well-posedness results, even in the weak sense, which is quite different from the well-studied "common noise" case. With the help of some structural assumptions on the observation equation, we are able to apply the localization argument to show that the weak solution exists and is unique in law.
We shall also mention some related problems, some of them actually motivated the study of such SDEs. These include a mean-field type stochastic control problems with partial observations and an extended form of the so-called Kyle-Back strategic insider trading equilibrium problem.
This talk is based on the joint works with Rainer Buckdahn and Juan Li.