Insider trading equilibrium in a market with memory

Abstract

We consider the Kyle-Back model for insider trading, with the difference that the classical Brownian motion noise of the noise traders is replaced by the noise of a fractional Brownian motion B H with Hurst parameter \({H>\frac{1}{2}}\) (when \({H=\frac{1}{2}, B^H}\) coincides with the classical Brownian motion). Heuristically, for \({H>\frac{1}{2}}\) this means that the noise traders has some “memory”, in the sense that any increment from time t on has a positive correlation with its value at t. (In other words, the noise trading is a persistent stochastic process). It also means that the paths of the noise trading process are more egular than in the classical Brownian motion case. We obtain an equation for the optimal (relative) trading intensity for the insider in this setting, and we show that when \({H\rightarrow\frac{1}{2}}\) the solution converges to the solution in the classical case. Finally, we discuss how the size of the Hurst coefficient H influences the optimal performance and portfolio of the insider.