SIAM Journal on Control and Optimization, Vol.56, No.2, 1154-1180, 2018
KYLE BACK EQUILIBRIUM MODELS AND LINEAR CONDITIONAL MEAN-FIELD SDEs
In this paper we study the Kyle Back strategic insider trading equilibrium model in which the insider has 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 an insider's information and the market price, and it is the first time being put into a rigorous mathematical framework of the recently developed conditional mean-field stochastic differential equation (CMFSDE). 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, and we substantiate the well-posedness of the resulting optimal closed-loop system, whence the existence of Kyle Back equilibrium.
Keywords:strategic insider trading;Kyle Back equilibrium;conditional mean-field SDEs;reference measures;optimal closed-loop system