Geodesic
A guaranteed deterministic approach to superhedging: the proprieties of semicontinuity and continuity of the Bellman--Isaacs equations
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 4, pp. 87-115

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A guaranteed deterministic problem setting of super-replication with discrete time is considered: the aim of hedging of a contingent claim is to ensure the coverage of possible payout under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compacts, that depend on the prehistory of prices: the increments of the price at each moment of time must lie in the corresponding compacts. The absence of transaction costs is assumed; the market is considered with trading constraints. The game-theoretical interpretation implies that the corresponding Bellman–Isaacs equations holds. In the present paper we propose several conditions for the solutions of these equations to be semicontinuous or continuous.
Keywords: guaranteed estimates, deterministic price dynamics, superreplication, Bellman–Isaacs equations, multi-valued mapping, semicontinuity, continuity
Mots-clés : option, robust condition of no arbitrage. 
@article{MGTA_2019_11_4_a5,
     author = {Sergey N. Smirnov},
     title = {A guaranteed deterministic approach to superhedging: the proprieties of semicontinuity and continuity of the {Bellman--Isaacs} equations},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {87--115},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2019_11_4_a5/}
}
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Sergey N. Smirnov. A guaranteed deterministic approach to superhedging: the proprieties of semicontinuity and continuity of the Bellman--Isaacs equations. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 4, pp. 87-115. http://geodesic.mathdoc.fr/item/MGTA_2019_11_4_a5/