[00603] Mean field stochastic control problems and related topics
Session Time & Room : 1C (Aug.21, 13:20-15:00) @E502
Type : Proposal of Minisymposium
Abstract : Mean-field (or, McKean-Vlasov) SDEs have been studied for a long time and have found lots of applications in different domains. Recently, with their pioneering seminal papers (2006-2007) on mean-field games and their applications in economics, finance and game theory, Lasry and Lions have given new impulses to this research topic, opened the way to new applications and attracted lots of researchers to this topic. One of these applications is the study of mean-field stochastic optimal control problems. In our symposium we will study the viability property for controlled mean-field flows, the mass-conserving SPDE coming from spatial mean-field term, etc.
[01320] Stochastic maximum principle for weighted mean-field system
Format : Talk at Waseda University
Author(s) :
Jie Xiong (Southern University of Science and Technology)
Abstract : We study the optimal control problem for a weighted mean-field system. A new feature of the control problem is that the coefficients depend on the state process as well as its weighted measure and the control variable. By applying variational technique, we establish a stochastic maximum principle. Also, we establish a sufficient condition of optimality. As an application, we investigate the optimal premium policy of an insurance firm for asset–liability management problem. This talk is based on a joint paper with Yanyan Tang.
[00653] The mass-conserving stochastic partial differential equaton coming from spatial mean-field term
Format : Talk at Waseda University
Author(s) :
Qi Zhang (Fudan University)
Abstract : In this talk, I will introduce our study about the mass-conserving stochastic partial differential equaiton. It is a kind of equation with spacial mean-field term such that its solution satisfies a mass-conservative property. We prove the existence and uniqueness of solution, and then construct a stationary solution by the nonlinear Feynman-Kac formula under Lipschitz assumption. Moreover, the existence of solution in the non-Lipschitz case is considered.
[01321] A quadratic mean-field BSDE with its applications
Format : Talk at Waseda University
Author(s) :
Huilin Zhang (Shandong University)
Abstract : In this talk I will introduce the well-posedness of a quadratic mean-field BSDE.
Moreover we show its several applications, in particular in the utility theory.
[01324] Mean field stochastic control under sublinear expectation
Format : Talk at Waseda University
Author(s) :
Juan Li (Shandong University)
Abstract : In this talk we study Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a SDE driven by a $G$-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the $G$-expectation. Also the associated cost functional is of mean-field type. We give a necessary optimality condition for control processes, and also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the $G$-expectation of parameterized random variables.
Based on joint work with Rainer Buckdahn (UBO, France), Bowen He (SDU, China).
