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Approximations and asymptotics of upper hedging prices in multinomial models


  • Ryuichi Nakajima
  • Masayuki Kumon
  • Akimichi Takemura
  • Kei Takeuchi


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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  • Ryuichi Nakajima & Masayuki Kumon & Akimichi Takemura & Kei Takeuchi, 2010. "Approximations and asymptotics of upper hedging prices in multinomial models," Papers 1007.4372,, revised Jun 2011.
  • Handle: RePEc:arx:papers:1007.4372

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    References listed on IDEAS

    1. Fausto Gozzi & Tiziano Vargiolu, 2002. "Superreplication of European multiasset derivatives with bounded stochastic volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 69-91, March.
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    Cited by:

    1. Vladimir Vovk, 2011. "Ito calculus without probability in idealized financial markets," Papers 1108.0799,, revised Aug 2014.

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