In this talk, we will study mean-field problems arising from switching diffusions. In contrast to the classical approach, the limit is characterized as the conditional distribution (given the history of the switching process) of the solution to a stochastic McKean-Vlasov differential equation with Markovian switching
[joint work with S.L. Nguyen and T.A. Hoang].
We will also develop an approach for solving
a class of non-traditional linear quadratic Gaussian (LQG) problems, in which the terminal cost is quadratic not with respect to the terminal state but with respect to
the measure associated with the terminal state [joint work with Y. Li, Q. Song, and F. Wu]. This problem then can be used as a benchmark example for solving high-dimensional HJB problems. Some preliminary results on numerical computation will be reported as well.
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