[1] Smirnov, S.N.: A Guaranteed deterministic approach to superhedging: financial market model, trading constraints, and the Bellman-Isaacs equations. Autom. Remote Control. 82, 722-743 (2021) [2] Föllmer, H., Schied, A.: Stochastic finance. An introduction in discrete time, 4th edn. Walter de Gruyter, New York (2016) [3] Bouchard, B., Nutz, M.: Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab. 25, 823-859 (2015) [4] Kolokoltsov, V.N.: Nonexpansive maps and option pricing theory. Kybernetika. 34, 713-724 (1998) [5] Bernhard, P., Engwerda, J.C., Roorda, B., Schumacher, J., Kolokoltsov, V., Saint-Pierre, P., Aubin, J.-P.: The Interval Market Model in Mathematical Finance: Game-Theoretic Methods. Springer, New York (2013) [6] Matsuda, T., Takemura, A.: Game-theoretic derivation of upper hedging prices of multivariate contingent claims and submodularity. Jpn. J. Indus Trial Appl. Math. 37, 213-248 (2020) [7] Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., Obƚój, J.: Pointwise arbitrage pricing theory in discrete time. Math. Op. Res. 44, 1034-1057 (2019) [8] Carassus, L., Vargiolu, T.: Super-replication price it can be ok. ESAIM Proc. Surv. 64, 54-64 (2018) [9] Smirnov, S.N.: A Guaranteed deterministic approach to superhedging: a game equilibrium in the case of no trading constraints. J. Math. Sci. 248, 105-115 (2020) [10] Carassus, L., Lépinette, E.: Pricing without no-arbitrage condition in discrete time. J. Math. Anal. Appl. 505, 125441 (2022) [11] Obƚój, J., Wiesel, J.: A unified framework for robust modelling of financial markets in discrete time. Finance Stoch. 25, 427-468 (2021) [12] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: no arbitrage properties of the market. Autom. Remote Control. 82, 172-187 (2021) [13] Smirnov, S.N.: Geometric criterion for a robust condition of no sure arbitrage with unlimited profit. Moscow Univ. Comput. Math. Cybern. 44, 146-150 (2020) [14] Jacod, J., Shiryaev, A.N.: Local martingales and the fundamental asset pricing theorems in the discrete-time case. Financ. Stochastics. 2, 259-273 (1998) [15] Smirnov, S.N.: Structural stability threshold for the condition of robust no deterministic sure arbitrage with unbounded profit. Moscow Univ. Comput. Math. Cybern. 45, 34-44 (2021) [16] Smirnov, S.N.: A guaranteed deterministic approach to the superhedging: semicontinuity and continuity properties of solutions of the Bellman-Isaacs equations. Autom. Remote Control. 82, 2024-2040 (2021) [17] Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis: Theory, Mathematics and Its Applications, vol. I. Springer, Berlin (1997) [18] Smirnov, S.N.: Guaranteed deterministic approach to superhedging: Lipschitz properties of solutions of the Bellman-Isaacs equations. In: Petrosyan, L., Mazalov, V., Zenkevich, N. (eds.) Frontiers of dynamic games. Static and dynamic game theory: Foundations and Applications. Birkhäuser Cham (2019) https://doi.org/10.1007/978-3-030-23699-1_14 [19] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: sensitivity of solutions of Bellman-Isaacs equations and numerical methods. Comput. Math. Model. 31, 384-401 (2020) [20] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: the relationship between the deterministic and stochastic problem statement without trading constraints. Theory Probab. Appl. 67, 548-569 (2023) [21] Carassus, L., Obƚój, J., Wiesel, J.: The robust superreplication problem: a dynamic approach. SIAM J. Financ. Math. 10, 907-941 (2019) [22] Carassus, L., Obƚój, J., Wiesel, J.: Erratum to The robust superreplication problem: a dynamic approach. SIAM J. Financ. Math. 13, 653-655 (2022) [23] Bertsekas, D.P., Shreve, S.E.: Stochastic Optimal Control: The Discrete-Time Case. Academic Press, New York (1978) [24] Smirnov, S.N.: A guaranteed deterministic approach to superhedging optimal mixed strategies of the market and their supports. In: Karapetyants, A.N., Pavlov, I.V., Shiryaev, A.N. (eds.) Operator Theory and Harmonic Analysis. Springer, Cham (2021) [25] Lange, K.L.: Borel sets of probability measures. Pacific J. Math. 48, 141-162 (1973) [26] Smirnov, S.N.: General theorem on a finite support of mixed strategy in the theory of zero-sum games. Doklady Math. 97, 215-218 (2018) |