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

Sergey Smirnov
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Sergey Smirnov: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1/52, 119991 Moscow, Russia

Mathematics, 2019, vol. 7, issue 12, 1-19

Abstract: 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.

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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