Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 128901-128901.doi: 10.1088/1674-1056/21/12/128901

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇    下一篇

Multidimensional subdiffusion model: Arbitrage-free market

李国华, 张红, 罗懋康   

  1. College of Mathematics, Sichuan University, Chengdu 610064, China
  • 收稿日期:2011-05-06 修回日期:2012-06-07 出版日期:2012-11-01 发布日期:2012-11-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

Multidimensional subdiffusion model: Arbitrage-free market

Li Guo-Hua (李国华), Zhang Hong (张红), Luo Mao-Kang (罗懋康)   

  1. College of Mathematics, Sichuan University, Chengdu 610064, China
  • Received:2011-05-06 Revised:2012-06-07 Online:2012-11-01 Published:2012-11-01
  • Contact: Luo Mao-Kang E-mail:makaluo@scu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

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摘要： To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα(t) for 0 < α <1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimensional subdiffusion process directed by the inverse α-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process by Laplace transform technique. Finally, using martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.

关键词: subordination, arbitrage-free, contingent claim valuation, fractional backward kolmogorov equation

Abstract: To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα(t) for 0 < α <1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimensional subdiffusion process directed by the inverse α-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process by Laplace transform technique. Finally, using martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.

Key words: subordination, arbitrage-free, contingent claim valuation, fractional backward kolmogorov equation

中图分类号:  (Economics; econophysics, financial markets, business and management)

  • 89.65.Gh
02.50.-r (Probability theory, stochastic processes, and statistics) 05.10.Gg (Stochastic analysis methods)