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

OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION
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DOI：
10.1142/s0219025703001432
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发表时间：
2003-12
期刊：
Infinite Dimensional Analysis, Quantum Probability and Related Topics
影响因子：
--
通讯作者：
Yaozhong Hu;B. Øksendal;A. Sulem
Yaozhong Hu;B. Øksendal;A. Sulem
中科院分区：
其他
文献类型：
--
作者：
Yaozhong Hu;B. Øksendal;A. Sulem

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本文建立了一个由分数布朗运动BH（t）驱动的具有Hurst参数的Black-Scholes市场的数学模型。关于BH（t）的积分的解释是Ito（Skorohod-Wick）的意义，而不是路径（已知会导致套利）。我们发现明确的最优消费率和最优投资组合在这样的市场中的代理与效用函数的权力型。当H → 1/2+时，所得结果收敛于标准布朗运动的相应结果.
We present a mathematical model for a Black–Scholes market driven by fractional Brownian motion BH(t) with Hurst parameter . The interpretation of the integrals with respect to BH(t) is in the sense of Ito (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.