OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION-Reference-Cited by-同舟云学术

OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION

Published:2003-12 Issue:04 Volume:06 Page:519-536
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

HU YAOZHONG¹,ØKSENDAL BERNT²³,SULEM AGNÈS⁴

Affiliation:

1. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142, USA

2. Department of Mathematics, University of Oslo, Box 1053 Blindern, N-0316 Oslo, Norway

3. Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway

4. INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France

Abstract

We present a mathematical model for a Black–Scholes market driven by fractional Brownian motion BH(t) with Hurst parameter [Formula: see text]. The interpretation of the integrals with respect to BH(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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025703001432

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