spacer
Purdue Computational Finance Program


Explicit Optimal Portfolio with Consumption in a Fractional Black-Scholes Market Using Logarithmic Utility

April 23, 2004
2:30 p.m.

BRNG B222

Mr. Yalcin Sarol and Mr. Tao Zhang, Ph.D. Students, Department of Mathematics, Purdue University, West Lafayette, Indiana

Abstract:
We consider the classical Merton problem of finding the optimal consumption rate and the optimal portfolio in a Black-Scholes market driven by fractional Brownian motion BH with Hurst parameter H>1/2. The interpretation of the integrals with respect to BH is in the sense of Skorohod, not pathwise which is known to lead to arbitrage. We find explicitly the optimal consumption rate, the optimal wealth process, and the optimal portfolio in such a market for an agent with logarithmic utility functions.
Purdue Memorial Union © 2003 Purdue University
Last Update: Apr 15, 2004
Please send comments and suggestions to the Webmaster.