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Open AccessFeature PaperArticle

A Guaranteed Deterministic Approach to Superhedging—The Case of Convex Payoff Functions on Options

1
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1/52, 119991 Moscow, Russia
2
Financial Engineering and Risk Management Laboratory, National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, 101000 Moscow, Russia
Mathematics 2019, 7(12), 1246; https://doi.org/10.3390/math7121246
Received: 29 July 2019 / Revised: 10 December 2019 / Accepted: 12 December 2019 / Published: 17 December 2019
(This article belongs to the Special Issue Mathematical Game Theory 2019)
This paper considers super-replication in a guaranteed deterministic problem setting with discrete time. The aim of hedging a contingent claim is to ensure the coverage of possible payoffs under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compacts that depend on the history of prices. The increments of the price at each moment in time must lie in the corresponding compacts. The absence of transaction costs is assumed. The game–theoretic interpretation of pricing American options implies that the corresponding Bellman–Isaacs equations hold for both pure and mixed strategies. In the present paper, we study some properties of the least favorable (for the “hedger”) mixed strategies of the “market” and of their supports in the special case of convex payoff functions. View Full-Text
Keywords: guaranteed estimates; deterministic price dynamics; super-replication; option; no arbitrage condition; Bellman-Isaacs equations; multi-valued mapping; semi-continuity; mixed strategies; game equilibrium; convex payoff functions guaranteed estimates; deterministic price dynamics; super-replication; option; no arbitrage condition; Bellman-Isaacs equations; multi-valued mapping; semi-continuity; mixed strategies; game equilibrium; convex payoff functions
MDPI and ACS Style

Smirnov, S. A Guaranteed Deterministic Approach to Superhedging—The Case of Convex Payoff Functions on Options. Mathematics 2019, 7, 1246.

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