指数半鞅模型中的均值修正鞅测度

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 932-941.

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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)

Abstract

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

CLC Number:

O211.6

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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References 16

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$\gamma$	$-0.3000$	$ -0.3500$	$ -0.4000$	$-0.4500 $	$-0.4577 $	$-0.5000 $
平凡边界	[0, 1]	[0, 1]	[0, 1]	[0, 1]	[0, 1]	[0, 1]
$[J_-, J_+]$	[0, 0.3297]	[0, 0.3624]	[0, 0.3935]	[0, 0.4231]	[0, 0.4263]	[0, 0.4512]
$C^{Q^{\alpha^*}}(K, T)$	0.4263	0.4263	0.4263	0.4263	0.4263	0.4263

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[2]	XIAO Shuang, JIAN Ming, CHEN Ai-Xiang, JIAN Bei. Fuzzy Pricing Formula for European Options with Jumps and Transaction Costs [J]. Acta mathematica scientia,Series A, 2015, 35(1): 118-130.
[3]	SUN Yu-Dong, SHI Xi-Min, WU Min. Barrier Options Pricing when Parameters Dependent on Stock Price [J]. Acta mathematica scientia,Series A, 2013, 33(5): 912-925.
[4]	Fei Wei-Yin. Large Deviations for \|Solutions to Stochastic Differential Equations Driven by Semimartingale with Non-Lipschitz Coefficients [J]. Acta mathematica scientia,Series A, 2009, 29(4): 1074-1083.
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Mean Correcting Martingale Measure for Exponential Semimartingale Market Models

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