Optimal Consumption and Portfolio in a Black–scholes Market Driven by Fractional Brownian Motion

We present a mathematical model for a Black–Scholes market driven by fractional Brownian motion B H (t) with Hurst parameter [Formula: see text]. The interpretation of the integrals with respect to B H (t) is in the sense of Itô (Skorohod–Wick), not pathwise (which is known to lead to arbitrage). We find explicitly the optimal consumption rate and the optimal portfolio in such a market for an agent with utility functions of power type. When H → 1/2+ the results converge to the corresponding (known) results for standard Brownian motion.