A~guaranteed deterministic approach to superhedging: the relationship
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 688-716
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We consider a guaranteed deterministic approach to the discrete-time
superreplication problem in which it is required to cover a contingent liability on a written option in all feasible scenarios. These scenarios are described by a priori given compact sets depending on the price history: at each time instant, the price increments must lie in the corresponding compact sets. We assume no transaction costs. The problem statement is game-theoretic and leads to the Bellman–Isaacs equations in pure and mixed “market”
strategies. In the case of no trading constraints, we study the relationship
between the Bellman functions in the “deterministic” and “probabilistic”
statements of the superhedging problem. As established under very general
conditions, the “probabilistic” Bellman function does not exceed the
“deterministic” counterpart. Sufficient conditions for their coincidence
are found.
Keywords:
guaranteed pricing, deterministic price dynamics, superhedging, American option, no arbitrage opportunities, the Bellman–Isaacs equations, set-valued mapping, mixed strategies, no trading constraints, risk-neutral measures, the generalized Snell envelope.
@article{TVP_2022_67_4_a3,
author = {S. N. Smirnov},
title = {A~guaranteed deterministic approach to superhedging: the relationship},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {688--716},
publisher = {mathdoc},
volume = {67},
number = {4},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a3/}
}
S. N. Smirnov. A~guaranteed deterministic approach to superhedging: the relationship. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 688-716. http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a3/