A Generalized Kyle-Back Strategic Insider Trading Model with Dynamic Information

TL;DR

This paper extends the Kyle-Back insider trading model to include dynamic information and non-Gaussian settings, using stochastic boundary value problems and filtering techniques to characterize equilibrium strategies.

Contribution

It introduces a generalized Kyle-Back model with dynamic information influenced by market prices, employing a novel approach with stochastic boundary value problems and filtering methods.

Findings

Characterization of equilibrium via stochastic boundary value problems

Use of filtering to determine pricing rules in non-Gaussian models

Conditions for affine solutions in the extended model

Abstract

In this paper we consider a class of generalized Kyle-Back strategic insider trading models in which the insider is able to use the dynamic information obtained by observing the instantaneous movement of an underlying asset that is allowed to be influenced by its market price. Since such a model will be largely outside the Gaussian paradigm, we shall try to Markovize it by introducing an auxiliary diffusion process, in the spirit of the weighted total order process of, e.g., \cite{CCD11}, as a part of the "pricing rule". As the main technical tool in solving the Kyle-Back equilibrium, we study a class of Stochastic Two-Point Boundary Value Problem (STPBVP), which resembles the dynamic Markovian bridge in the literature, but without insisting on its local martingale requirement. In the case when the solution of the STPBVP has an affine structure, we show that the pricing rule functions, whence the Kyle-Back equilibrium, can be determined by the decoupling field of a forward-backward SDE obtained via a non-linear filtering approach, along with a set of compatibility conditions.