Guaranteed Deterministic Approach to Superhedging: Mixed Strategies and Game Equilibrium.

Smirnov, S. N.

For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure the cheapest coverage of the contingent claim on an option under all scenarios that are set using a priori defined compacts depending on the price history. Price increments at each moment of time must lie in the corresponding compact sets. We consider a market with trading constraints and no 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.

STRATEGY games; NASH equilibrium; PRICES; TRANSACTION costs; SET-valued maps

Automation & Remote Control, 2022, Vol 83, Issue 12, p2019

0005-1179

Academic Journal

10.1134/S0005117922012013X