一类带跳的时滞Black-Scholes模型  

A class of delay Black-Scholes model with jump

作　　者：张庆华[1] 薛大威[2,3] 闫理坦[1,3] 

机构地区：[1]东华大学旭日工商管理学院,上海200051 [2]上海兴业全球基金管理有限公司专户投资部,上海200122 [3]东华大学理学院,上海200051

出　　处：《黑龙江大学自然科学学报》2015年第2期141-149,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11171062);上海市教育委员会科研创新项目资助(12ZZ063);东华大学博士创新基金资助项目(CUSF-DH-D-2013038)

摘　　要：研究一类由Lévy过程驱动的时滞随机微分方程,在对Lévy过程的跳以及方程系数的一些正则性条件限制下,证明该方程是适定的,并可作为描述股票价格变化的市场模型。综合考虑时滞,该模型能够在一定程度上描述资产价格的趋势效应。由于该模型所描述的市场是不完备的,故利用Fllmer-Schweizer最小鞅测度,构造一类欧式看涨期权定价公式。A class of delay stochastic differential equations driven by Lévy process is studied. It is proved that these equations are well posed under some regular conditions on coeffivients and Levy process with jump, so it can be used to illustrate the changes of stock price. Synthesize the delay effect, this kind of models could also describe the trend effect of asset price. Note that Lévy model corresponds to incomplete market, a Black-Scholes pricing formula for European call option is constructed by using Follmer-Schwei- zer minimal measure.

关 键 词：BLACK-SCHOLES公式 最小鞅测度 LÉVY过程 带跳随机时滞微分方程 

分 类 号：O211.9[理学—概率论与数理统计]