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Mat. Teor. Igr Pril., 2020, Volume 12, Issue 1, Pages 60–90 (Mi mgta254)  

This article is cited in 1 scientific paper (total in 1 paper)

A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium

Sergey N. Smirnov

Department of System Analysis, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University

Abstract: For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a cheapest coverage of the contingent claim on an option under all scenarios which are set using a priori defined compacts, depending on the price history: price increments at each moment of time must lie in the corresponding compacts. The market is considered with trading constraints and without transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman–Isaacs equations. In this article, we introduce a mixed extension of the “market” pure strategies. Several results concerning game equilibrium are obtained.

Keywords: guaranteed estimates, deterministic price dynamics, super-replication, option, arbitrage, absence of arbitrage opportunities, Bellman–Isaacs equations, multivalued mapping, mixed strategies, game equilibrium.

Full text: PDF file (206 kB)
References: PDF file   HTML file
UDC: 519.866.2
BBK: 22.18
Received: 03.06.2019
Revised: 10.11.2019
Accepted:23.12.2019

Citation: Sergey N. Smirnov, “A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium”, Mat. Teor. Igr Pril., 12:1 (2020), 60–90

Citation in format AMSBIB
\Bibitem{Smi20}
\by Sergey~N.~Smirnov
\paper A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium
\jour Mat. Teor. Igr Pril.
\yr 2020
\vol 12
\issue 1
\pages 60--90
\mathnet{http://mi.mathnet.ru/mgta254}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sergei N. Smirnov, “Garantirovannyi deterministskii podkhod k superkhedzhirovaniyu: naibolee neblagopriyatnye stsenarii povedeniya rynka i problema momentov”, MTIP, 12:3 (2020), 50–88  mathnet
  • Математическая теория игр и её приложения
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