指数半鞅模型中的均值修正鞅测度  

Mean Correcting Martingale Measure for Exponential Semimartingale Market Models

作　　者：姚落根 杨刚 杨向群 Yao Luogen;Yang Gang;Yang Xiangqun(School of Mathematics and Statistics, Hunan University of Commerce, Changsha 410205;College of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha 410205)

机构地区：[1]湖南商学院数学与统计学院,长沙410205 [2]湖南财政经济学院数学与统计学院,长沙410205

出　　处：《数学物理学报（A辑）》2019年第4期932-941,共10页Acta Mathematica Scientia

基　　金：湖南省自然科学基金(2019JJ40141,2017JJ2127);国家社会科学基金(15BJY122);湖南省教育厅优秀青年基金(16B141)~~

摘　　要：在半鞅模型中,利用均值修正变换构造了一个鞅测度.在半鞅存在连续的局部鞅时,证明了该鞅测度是均值修正鞅测度.对纯跳半鞅,虽然该鞅测度与市场概率不等价,但在无套利区间能达到平凡边界时,证明了具有凸收益函数的期权在该鞅测度下的价格仍然无套利.A martingale measure is constructed by using a mean correcting transform in a general semimartingale market model.It is shown that this measure is the mean correcting martingale measure if the semimartingale exists a continuous local martingale part.Although this measure cannot be equivalent to the physical probability for a pure jump semimartingale process,we show that option price of a European option with a convex payoff function under this measure is still arbitrage free if the arbitrage-free interval can reach universal bounds.

关 键 词：半鞅 均值修正鞅测度 期权定价 

分 类 号：O211.6[理学—概率论与数理统计]