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
李国华, 张红, 罗懋康
Li Guo-Hua (李国华), Zhang Hong (张红), Luo Mao-Kang (罗懋康)
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.
中图分类号: (Economics; econophysics, financial markets, business and management)