Two-price conic Kyle model

A market microstructure model with fundamental market illiquidity is introduced by incorporating the lower and upper prices of a risky asset using two-price conic finance theory. Information asymmetry is captured by considering an informed trader and uninformed traders. Under the premise that there is a limit in the risk a financial market can accept, the (informed and uninformed) traders sell the risky asset to the market at the lower price and buy it from the market at the upper price. Sets of acceptable risks to the market, which are called market cones, are introduced from which the lower and upper prices are obtained. Three market cones are considered, and they are specified by three transformations, namely the Esscher transform, the Wang transform, and the Girsanov transform, to introduce the underlying probability measures supporting the market cones. The informed trader aims to determine an optimal demand on the risky asset by maximizing the expected profit. For each of the three market cones, piecewise linear equilibria for the buy side and the sell side are obtained in a single-auction model. Numerical examples are provided to illustrate piecewise linear equilibria.