Kyle-Back's model with Lévy noise

Abstract

The continuous-time version of Kyle's [6] model, known as the Back's [2] model, of asset pricing with asymmetric information, is studied. A larger class of price processes and a larger classes of noise traders' processes are studied. The price process, as in Kyle's [6] model, is allowed to depend on the path of the market order. The process of the noise traders' is considered to be an inhomogeneous Lévy process. The solutions are found with the use of the Hamilton-Jacobi-Bellman equations. With the informed agent being risk-neutral, the price pressure is constant over time, and there is no equilibirium in the presence of jumps. If the informed agent is risk-averse, there is no equilibirium in the presence of either jumps or drift in the process of the noise traders'.