Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications
Published Online:17 Jul 2019https://doi.org/10.1287/moor.2019.0989
References
- [1] (2006) Infinite Dimensional Analysis (Springer-Verlag, Berlin).Google Scholar
- [2] (2017) Optimal consumption and investment with fixed and proportional transaction costs. SIAM J. Control Optim. 51(3):1673–1710.Crossref, Google Scholar
- [3] (2017) A zero-sum stochastic differential game with impulses, precommitment, and unrestricted cost functions. Appl. Math. Optim. 79(2):483–514.Crossref, Google Scholar
- [4] (2016) Weakly chained matrices, policy iteration, and impulse control. SIAM J. Numer. Anal. 54(3):1341–1364.Crossref, Google Scholar
- [5] (2018) Convergence of implicit schemes for Hamilton–Jacobi–Bellman quasi-variational inequalities. SIAM J. Control Optim. 56(6):3994–4016.Crossref, Google Scholar
- [6] (2016) Topics in stochastic control and differential game theory, with application to mathematical finance. Unpublished doctoral thesis, University of Padova, Padova, Italy.Google Scholar
- [7] (2017) A general verification result for stochastic impulse control problems. SIAM J. Control Optim. 55(2):627–649.Crossref, Google Scholar
- [8] (1977) Nonzero-sum stochastic differential games with stopping times and free boundary problems. Trans. Amer. Math. Soc. 231(2):275–327.Crossref, Google Scholar
- [9] (1982) Contrôle Impulsionnel et Inéquations Quasi Variationnelles, Méthodes Mathématiques de l'Informatique, vol. 11 (Dunod, Paris).Google Scholar
- [10] (2016) On classical and restricted impulse stochastic control for the exchange rate. Appl. Math. Optim. 74(2):423–454.Crossref, Google Scholar
- [11] (2004) Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Control Optim. 43(2):624–642.Crossref, Google Scholar
- [12] (2000) Classical and impulse stochastic control of the exchange rate using interest rates and reserves. Math. Finance 10(2):141–156.Crossref, Google Scholar
- [13] (2015) Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. J. Indust. Management Optim. 11(1):27–40.Crossref, Google Scholar
- [14] (2013) Maximum principle for non-zero sum differential games of BSDEs involving impulse controls. 32nd Chinese Control Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 1564–1569.Google Scholar
- [15] (2013) A nonzero-sum game approach to convertible bonds: Tax benefit, bankruptcy cost, and early/late calls. Math. Finance 23(1):57–93.Crossref, Google Scholar
- [16] (2012) Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities. SIAM J. Control Optim. 51(3):2102–2131.Crossref, Google Scholar
- [17] (2018) Stochastic nonzero-sum games: A new connection between singular control and optimal stopping. Adv. Appl. Probab. 50(2):347–372.Crossref, Google Scholar
- [18] (2018) Nash equilibria of threshold type for two-player nonzero-sum games of stopping. Ann. Appl. Probab. 28(1):112–147.Crossref, Google Scholar
- [19] (2018) Zero-sum stochastic differential game in finite horizon involving impulse controls. Appl. Math. Optim., ePub ahead of print, September 24, https://doi.org/10.1007/s00245-018-9529-2.Crossref, Google Scholar
- [20] (1972) The Existence of Value in Differential Games, Memoirs of the American Mathematical Society, vol. 126 (American Mathematical Society, Providence, RI).Google Scholar
- [21] (1989) On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J. 38(2):293–314.Crossref, Google Scholar
- [22] (1973) Stochastic games and variational inequalities. Arch. Rational Mechanics Anal. 51(5):321–346.Crossref, Google Scholar
- [23] (2003) Stochastic Differential Equations (Springer-Verlag, Berlin).Crossref, Google Scholar
- [24] (2007) Applied Stochastic Control of Jump Diffusions, 2nd ed. (Springer-Verlag, Berlin).Crossref, Google Scholar
- [25] (1982) Zero-sum Markov games with stopping and impulsive strategies. Appl. Math. Optim. 9(1):1–24.Crossref, Google Scholar
- [26] (2011) Stochastic differential games involving impulse controls. ESAIM: Control Optim. Calculus Variations 17(3):749–760.Crossref, Google Scholar

