A Guaranteed Deterministic Approach to Superhedging: No Arbitrage Properties of the Market.

Smirnov, S. N.

For a discrete-time super-replication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a complete coverage of contingent claims on an option under all admissible scenarios. These scenarios are specified using a priori defined compact sets, depending on the price prehistory: at each time step the price increments must belong to the corresponding compact sets. The market is considered with trading constraints and without transaction costs. The problem statement is game-theoretic in nature and directly yields the Bellman–Isaacs equations. This paper is focused on several concepts formalizing the no arbitrage property of the market within the deterministic approach as well as on their properties. A new concept of robustness (structural stability) of the no arbitrage properties of the market is introduced.

Automation & Remote Control, 2021, Vol 82, Issue 1, p172

0005-1179

Academic Journal

10.1134/S0005117921010124