| 混合分数债券市场中的套利和马尔科夫问题 |
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| 引用本文： | 李程程,闫理坦.混合分数债券市场中的套利和马尔科夫问题[J].苏州科技学院学报(自然科学版),2009,26(3):6-13. |
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| 作者姓名： | 李程程 闫理坦 |
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| 作者单位： | 东华大学理学院,上海,201620 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究了基于混合分数布朗运动的债券市场上的价格预测、马尔科夫短期利率和套利问题。根据布朗运动和分数布朗运动的性质以及计算方法，推导出了在风险中性度量下的债券价格的预测方程，证明了马尔科夫短期利率成立的充要条件，找到了可以实现套利的资产组合。
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| 关 键 词： | 分数布朗运动 混合分数布朗运动 债券市场 马尔科夫短期利率 组合与套利 |
On Arbitrage and Markovian Short Rates in Mixed Fractional Bond Markets |
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| LI Cheng-cheng,YAN Li-tan.On Arbitrage and Markovian Short Rates in Mixed Fractional Bond Markets[J].Journal of University of Science and Technology of Suzhou,2009,26(3):6-13. |
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| Authors: | LI Cheng-cheng YAN Li-tan |
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| Institution: | (College of Science, Donghua University, Shanghai 201620, China) |
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| Abstract: | In this article, we focus on the prediction for bond price, arbitrage and Markovian short rates in the bond markets based on mixed fractional Brownian motion. By using the properties and calculation method in the related theory of Brownian motion and fractional Brownian motion, we have derived the prediction formula for bond price, and have proved the sufficient and necessary condition for Markovian short interest rates. Meanwhile, a portfolio capable of realizing the arbitrage is given. |
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| Keywords: | fractional Brownian motion mixed fractional Brownian motion bond market Markovian short rates portfolio and arbitrage |
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