## Kyle-Back Equilibrium Models and Linear Conditional Mean-field SDEs. (arXiv:1711.03223v1 [math.PR])

In this paper we study the Kyle-Back strategic insider trading equilibrium
model in which the insider has an instantaneous information on an asset,
assumed to follow an Ornstein-Uhlenback-type dynamics that allows possible
influence by the market price. Such a model exhibits some further interplay
between insider's information and the market price, and it is the first time
being put into a rigorous mathematical framework of the recently developed {\it
conditional mean-field} stochastic differential equation (CMFSDEs). With the
help of the "reference probability measure" concept in filtering theory, we
shall first prove a general well-posedness result for a class of linear
CMFSDEs, which is new in the literature of both filtering theory and mean-field
SDEs, and will be the foundation for the underlying strategic equilibrium
model. Assuming some further Gaussian structures of the model, we find a closed
form of optimal intensity of trading strategy as well as the dynamic pricing
rules. W查看全文