Continuous auctions and insider trading: uniqueness and risk aversion
The Kyle and Back model of continuous time asset pricing with asymmetric information is studied (see [\textit{A. S. Kyle}, Econometrica 53, 1315--1335 (1985; Zbl 0571.90010); \textit{K. Black}, Rev. Financial Stud. 5, 387--409 (1992)]). The author allows the price to take into account the history of cumulative market orders. It is shown that no expected (or inconspicuous insider) trade theorem is verified in equilibrium, i.e., the market expectation regarding the informed trading is zero regardless of how much the informed agent is sensitive to the risk. Two types of utility functions are considered: the identity function (risk-neutral) and a negative-exponential function (risk-averse). When the informed agent is risk-neutral, there is a unique equilibrium in which the price pressure is constant over time and the price depends only on the cumulative market order. In contrast, when the informed agent is risk-averse, the price pressure decreases over time and the price depends on the whole path. Optimality conditions and equilibrium pricing rules are considered. It is proved that the equilibrium with risk-aversion converges to the risk-neutral equilibrium as the degree of risk aversion goes to zero.
scientific article; zbMATH DE number 2059099