A multidimensional subdiffusion model:An arbitrage-free market  

作　　者：李国华 张红 罗懋康 

机构地区：[1]College of Mathematics,Sichuan University

出　　处：《Chinese Physics B》2012年第12期561-567,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.11171238)

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 multidimen- sional subdiffusion process directed by the inverse a-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 using the Laplace transform technique. Finally, using a 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.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 multidimen- sional subdiffusion process directed by the inverse a-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 using the Laplace transform technique. Finally, using a 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 Kol-mogorov equation 

分 类 号：O175[理学—数学] F830.9[理学—基础数学]