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The Relations between Minimal Martingale Measure and Minimal Entropy Martingale Measure

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Abstract

We consider incomplete markets, where each risky asset fluctuation is a continuous semimartingale, and study a subset of Equivalent Local Martingale Measures in which Minimal Martingale Measure minimizes relative entropy.We also discuss, as special cases, some models with the risky assetfluctuation represented as a solution of some stochastic differential equations.Finally, we mention that the predictable representation property is essentialin order that Minimal Martingale Measure coincides with Minimal Entropy Martingale Measure.

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  1. Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama, 223-8522, Japan

    Takuji Arai

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  1. Takuji Arai
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Arai, T. The Relations between Minimal Martingale Measure and Minimal Entropy Martingale Measure. Asia-Pacific Financial Markets 8, 167–177 (2001). https://doi.org/10.1023/A:1011984313198

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