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Approximations and asymptotics of upper hedging prices in multinomial models

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Abstract

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of the Black–Scholes–Barenblatt equation.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan

    Ryuichi Nakajima & Akimichi Takemura

  2. Japanese Association for Promoting Quality Assurance in Statistics, Tokyo, Japan

    Masayuki Kumon

  3. Graduate School of Economics, University of Tokyo, Tokyo, Japan

    Kei Takeuchi

Authors
  1. Ryuichi Nakajima
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  2. Masayuki Kumon
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  3. Akimichi Takemura
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  4. Kei Takeuchi
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Correspondence to Akimichi Takemura.

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Nakajima, R., Kumon, M., Takemura, A. et al. Approximations and asymptotics of upper hedging prices in multinomial models. Japan J. Indust. Appl. Math. 29, 1–21 (2012). https://doi.org/10.1007/s13160-011-0047-8

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  • DOI: https://doi.org/10.1007/s13160-011-0047-8

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