Open AccessA guaranteed deterministic approach to superhedging: most unfavorable scenarios of market behaviour and moment problem
Author(s) -
С. Н. Смирнов,
Sergey Sergey
Publication year - 2020
Publication title -
matematičeskaâ teoriâ igr i eë priloženiâ
Language(s) - English
Resource type - Journals
ISSN - 2074-9872
DOI - 10.17076/mgta_2020_3_21
Subject(s) - moment (physics) , mathematical economics , a priori and a posteriori , class (philosophy) , mathematical optimization , replication (statistics) , transaction cost , mathematics , database transaction , economics , computer science , microeconomics , statistics , philosophy , physics , epistemology , classical mechanics , artificial intelligence , programming language
A guaranteed deterministic problem setting of super-replication with discrete time is considered: the aim of hedging of a contingent claim is to ensure the coverage of possible payout under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compacts, that depend on the prehistory of prices: the increments of the price at each moment of time must lie in the corresponding compacts. The absence of transaction costs is assumed. The game-theoretical interpretation implies that the corresponding Bellman-Isaac equations hold, both for pure and mixed strategies. In the present paper, we propose a two-step method of solving the Bellman equation arising in the case of (game) equilibrium. In particular, the most unfavorable strategies of the `market can be found in the class of the distributions concentrated at most in n+1 point, where n is the number of risky assets.