Financial Markets with Memory II: Innovation Processes and Expected Utility Maximization

Abstract

Abstract We develop a prediction theory for a class of processes with stationary increments. In particular, we prove a prediction formula for these processes from a finite segment of the past. Using the formula, we prove an explicit representation of the innovation processes associated with the stationary increments processes. We apply the representation to obtain a closed-form solution to the problem of expected logarithmic utility maximization for the financial markets with memory introduced by the first and second authors.