Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (1): 35-50.doi: 10.1007/s40305-023-00490-4

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A Note on Transition Kernels for the Most Unfavourable Mixed Strategies of the Market

Sergey N. Smirnov   

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russian Federation, 119991
  • Received:2023-01-07 Revised:2023-04-17 Online:2024-03-30 Published:2024-03-13
  • Contact: Sergey N. Smirnov E-mail:s.n.smirnov@gmail.com
  • Supported by:
    This work was was supported by Moscow Center of Fundamental and Applied Mathematics (No.75-15-2022-284).

Abstract: We consider a deterministic model of market evolution with trading constraints and apply a game-theoretic approach to the superhedging problem. We obtain sufficient conditions for the game equilibrium and prove under these conditions the existence of a Borel-measurable transition kernel describing dependence on price prehistory of the most unfavourable mixed strategy of the market.

Key words: Superhedging, Guaranteed deterministic approach, Optimal mixed strategies of the market, Borel-measurable transition kernel, Game equilibrium

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