指数半鞅模型中的均值修正鞅测度

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 932-941.

指数半鞅模型中的均值修正鞅测度

姚落根¹(),杨刚^1,*(),杨向群²()

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

收稿日期:2017-12-13 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 杨刚 E-mail:yaoluogen@sina.com;yanggangmath@sina.com;xqyang@hunnu.edu.cn
作者简介:姚落根, E-mail:yaoluogen@sina.com|杨向群, E-mail:xqyang@hunnu.edu.cn
基金资助:
湖南省自然科学基金(2019JJ40141);湖南省自然科学基金(2017JJ2127);国家社会科学基金(15BJY122);湖南省教育厅优秀青年基金(16B141)

Mean Correcting Martingale Measure for Exponential Semimartingale Market Models

Luogen Yao¹(),Gang Yang^1,*(),Xiangqun Yang²()

¹ School of Mathematics and Statistics, Hunan University of Commerce, Changsha 410205
² College of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha 410205

Received:2017-12-13 Online:2019-08-26 Published:2019-09-11
Contact: Gang Yang E-mail:yaoluogen@sina.com;yanggangmath@sina.com;xqyang@hunnu.edu.cn
Supported by:
the Natural Science Foundation of Hunan Province(2019JJ40141);the Natural Science Foundation of Hunan Province(2017JJ2127);the National Social Science Fund of China(15BJY122);the Excellent Youth Foundation of Hunan Provincial Department of Education(16B141)

摘要/Abstract

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.

关键词: 半鞅, 均值修正鞅测度, 期权定价

Abstract:

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.

Key words: Semimartingale, Mean correcting martingale measure, Option pricing

中图分类号:

O211.6

姚落根,杨刚,杨向群. 指数半鞅模型中的均值修正鞅测度[J]. 数学物理学报, 2019, 39(4): 932-941.

Luogen Yao,Gang Yang,Xiangqun Yang. Mean Correcting Martingale Measure for Exponential Semimartingale Market Models[J]. Acta mathematica scientia,Series A, 2019, 39(4): 932-941.

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