A Guaranteed Deterministic Approach to Superhedging: Financial Market Model, Trading Constraints, and the Bellman–Isaacs Equations.

Smirnov, S. N.

A guaranteed deterministic problem setting of superreplication in discrete time is proposed as an alternative to the traditional probabilistic approach based on the use of the reference measure. Within the proposed framework, the reference measure is not needed, and aim of hedging of contingent claim is to guarantee coverage of possible payoff under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compact sets, that depend on the prehistory of prices: the increments of the price at each moment of time must lie in the corresponding compact sets. The presentation focuses on achieving clarity, without aiming the greatest possible generality; this is the reason for the nature of a number of assumptions. The absence of transaction costs is assumed, and the market is considered both with and without trade constraints. The game-theoretic approach immediately allows us to write down the corresponding Bellman–Isaacs equations using economic interpretation of the problem.

FINANCIAL markets; TRANSACTION costs; EQUATIONS; SET-valued maps; DETERMINISTIC algorithms

Automation & Remote Control, 2021, Vol 82, Issue 4, p722

0005-1179

Academic Journal

10.1134/S0005117921040081