An important class of random walks includes those in which the random increment at time step t depends on the complete history of the process. We consider a recently proposed discrete-time non-Markovian random walk process characterized by a memory parameter p. We numerically calculate the first...

In this paper we present a method for determining optimal trading strategies for Itô diffusion processes. By framing the problem in terms of the first passage time for the process we derive distribution and density functions for the trade length and use these functions to calculate the expected...