El Farouq, Naïma; Barles, Guy; Bernhard, Pierre Deterministic minimax impulse control. (English) Zbl 1198.49025 Appl. Math. Optim. 61, No. 3, 353-378 (2010). Summary: We prove the uniqueness of the viscosity solution of an Isaacs quasi-variational inequality arising in an impulse control minimax problem, motivated by an application in mathematical finance. Cited in 11 Documents MSC: 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49N25 Impulsive optimal control problems 49N70 Differential games and control 49J40 Variational inequalities Keywords:impulse control; robust control; differential games; quasi-variational inequality; viscosity solution PDFBibTeX XMLCite \textit{N. El Farouq} et al., Appl. Math. Optim. 61, No. 3, 353--378 (2010; Zbl 1198.49025) Full Text: DOI References: [1] Bardi, M., Capuzzo-Dolcetta, I.: Optimal and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhaüser, Basel (1997) [2] Barles, G.: Solutions de Viscosité des Équations de Hamilton-Jacobi. Mathématiques & Applications. Springer, Berlin, Heidelberg, New York (1994) [3] Barles, G.: Deterministic impulse control problems. SIAM J. Control Optim. 23, 419–432 (1985) · Zbl 0571.49020 · doi:10.1137/0323027 [4] Bernhard, P.: A robust control approach to option pricing including transaction costs. In: Annals of the ISDG, vol. 7, pp. 391–416. Birkhaüser, Basel (2005) · Zbl 1181.91309 [5] Bernhard, P., El Farouq, N., Thiery, S.: An impulsive differential game arising in finance with interesting singularities. In: Annals of the ISDG, vol. 8, pp. 335–363. Birkhaüser, Basel (2006) · Zbl 1274.91068 [6] Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 177, 1–42 (1983) · Zbl 0599.35024 · doi:10.1090/S0002-9947-1983-0690039-8 [7] Dharmatti, S., Shaiju, A.J.: Infinite dimensional differential games with hybrid controls. Proc. Indian Acad. Sci. Math. 117, 233–257 (2007) · Zbl 1293.91021 · doi:10.1007/s12044-007-0019-8 [8] Dharmatti, S., Ramaswamy, M.: Zero-sum differential games involving hybrid controls. J. Optim. Theory Appl. 128, 75–102 (2006) · Zbl 1099.91022 · doi:10.1007/s10957-005-7558-x [9] Evans, L.C., Souganidis, P.E.: Differential games and representation formulas for the solution of Hamilton-Jacobi-Isaacs equations. Indiana Univ. J. Math. 33, 773–797 (1984) · Zbl 1169.91317 · doi:10.1512/iumj.1984.33.33040 [10] Fleming, W.H.: The convergence problem for differential games, 2. Ann. Math. Study 52, 195–210 (1964) · Zbl 0137.14204 [11] Lions, P.L.: Generalized Solutions of Hamilton-Jacobi Equations. Pitman, London (1982) · Zbl 0497.35001 [12] Lions, P.L., Souganidis, P.E.: Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations. SIAM J. Control Optim. 23, 566–583 (1985) · Zbl 0569.49019 · doi:10.1137/0323036 [13] Shaiju, A.J., Dharmatti, S.: Differential games with continuous, switching and impulse controls. Nonlinear Anal. 63, 23–41 (2005) · Zbl 1132.91356 · doi:10.1016/j.na.2005.04.002 [14] Souganidis, P.E.: Max-min representations and product formulas for the viscosity solutions of Hamilton-Jacobi equations with applications to differential games. Nonlinear Anal. Theory Methods Appl. 9, 217–257 (1985) · Zbl 0554.35016 · doi:10.1016/0362-546X(85)90062-8 [15] Yong, J.M.: Zero-sum differential games involving impulse controls. Appl. Math. Optim. 29, 243–261 (1994) · Zbl 0808.90142 · doi:10.1007/BF01189477 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.