Guaranteed Deterministic Approach to Superhedging: the Semicontinuity and Continuity Properties of Solutions of the Bellman–Isaacs Equations.

Smirnov, S. N.

We consider a guaranteed deterministic statement of the problem of discrete-time superreplication: the aim of hedging a contingent claim is to ensure the coverage of possible payout under the option contract for all feasible scenarios. These scenarios are given by a priori given compact sets that depend on the price history: the price increments at each time must lie in the corresponding compact sets. The lack of transaction costs is assumed; the market with trading constraints is considered. The game-theoretic interpretation implies that the corresponding Bellman–Isaacs equations hold. In the present paper, we propose several conditions for the solutions of these equations to be semicontinuous or continuous.

EQUATIONS; CONTINUITY; TRANSACTION costs; SET-valued maps

Automation & Remote Control, 2021, Vol 82, Issue 11, p2024

0005-1179

Academic Journal

10.1134/S0005117921110163