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 Yang1,*(),Xiangqun Yang2()   

  1. 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;;
  • 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)


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