An Optimal Portfolio Problem Presented by Fractional Brownian Motion and Its Applications

We use the dynamic programming principle method to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function, and solve the optimal portfolio problem explicitly in a Black-Scholes type of market driven by fractional Brownian motion with Hurst parameter H∈(0,1). The results are compared with the corresponding well-known results in the standard Black-Scholes market (H=1/2). As an application of our proposed model, two optimal problems are discussed and solved, analytically