N-Player Stochastic Differential Games with Regime Switching and Mean Field Convergence

References

• [1] Bayraktar E, Cecchin A, Chakraborty P (2023) Mean field control and finite agent approximation for regime-switching jump diffusions. Appl. Math. Optim. 88(2):36.Crossref, Google Scholar
• [2] Bensoussan A, Frehse J (2000) Stochastic games for N players. J. Optim. Theory Appl. 105(3):543–565.Crossref, Google Scholar
• [3] Bensoussan A, Frehse J, Yam SCP (2013) Mean Field Games and Mean Field Type Control Theory, vol. 101 (Springer, Berlin).Crossref, Google Scholar
• [4] Bensoussan A, Djehiche B, Tembine H, Yam SCP (2020) Mean-field-type games with jump and regime switching. Dynam. Games Appl. 10:19–57.Crossref, Google Scholar
• [5] Bensoussan A, Sung KCJ, Yam SCP, Yung SP (2016) Linear-quadratic mean field games. J. Optim. Theory Appl. 169:496–529.Crossref, Google Scholar
• [6] Bierbrauer M, Trück S, Weron R (2004) Modeling electricity prices with regime switching models. Bubak M, van Albada GD, Sloot PMA, Dongarra J, eds. Comput. Sci.—ICCS 2004, Lecture Notes in Computer Science, vol. 3039 (Springer, Berlin), 859–867.Google Scholar
• [7] Borkar VS, Ghosh MK (1992) Stochastic differential games: Occupation measure based approach. J. Optim. Theory Appl. 73(2):359–385.Crossref, Google Scholar
• [8] Cardaliaguet P, Delarue F, Lasry JM, Lions PL (2019) The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Princeton University Press, Princeton, NJ).Google Scholar
• [9] Carmona R (2021) Applications of mean field games in financial engineering and economic theory. Delarue F, ed. Mean Field Games on Agent Based Models to Nash Equilibria, AMS 2020, vol. 78 (American Mathematical Society, Providence, RI), 165–219.Google Scholar
• [10] Carmona R, Delarue F (2013) Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4):2705–2734.Crossref, Google Scholar
• [11] Carmona R, Delarue F (2018) Probabilistic Theory of Mean Field Games with Applications I (Springer, Cham, Switzerland).Crossref, Google Scholar
• [12] Carmona R, Delarue F (2018) Probabilistic Theory of Mean Field Games with Applications II (Springer, Cham, Switzerland).Crossref, Google Scholar
• [13] Carmona R, Delarue F, Lacker D (2016) Mean field games with common noise. Ann. Probab. 44(6):3740–3803.Crossref, Google Scholar
• [14] Delarue F (2003) Estimates of the solutions of a system of quasi-linear PDEs. A probabilistic scheme. Azéma J, Émery M, Ledoux M, Yor M, eds. Séminaire de Probabilités XXXVII, Lecture Notes in Mathematics, vol. 1832 (Springer, Berlin), 290–332.Crossref, Google Scholar
• [15] Djehiche B, Tcheukam A, Tembine H (2017) Mean-field-type games in engineering. AIMS Electronics Electrical Engrg. 1(1):18–73.Crossref, Google Scholar
• [16] Elias RS, Wahab MIM, Fang L (2014) A comparison of regime-switching temperature modeling approaches for applications in weather derivatives. Eur. J. Oper. Res. 232(3):549–560.Crossref, Google Scholar
• [17] Elliott RJ, Siu TK (2010) On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. Ann. Oper. Res. 176:271–291.Crossref, Google Scholar
• [18] Elliott RJ, Siu TK (2011) A stochastic differential game for optimal investment of an insurer with regime switching. Quant. Finance 11(3):365–380.Crossref, Google Scholar
• [19] Friedman A (1972) Stochastic differential games. J. Differential Equations 11(1):79–108.Crossref, Google Scholar
• [20] Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Comm. Inform. Systems 6(1):221–252.Google Scholar
• [21] Jian J, Lai P, Song Q, Ye J (2024) The convergence rate of the equilibrium measure for the hybrid LQG mean field game. Nonlinear Anal. Hybrid Systems 52:101454.Crossref, Google Scholar
• [22] Ladyzhenskaia OA, Solonnikov VA, Ural’tseva NN (1968) Linear and Quasi-Linear Equations of Parabolic Type, vol. 23 (Americal Mathematical Society, Providence, RI).Crossref, Google Scholar
• [23] Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [24] Li Y, Cui L, Lin C (2017) Modeling and analysis for multi-state systems with discrete-time Markov regime-switching. Reliability Engrg. System Safety 166:41–49.Crossref, Google Scholar
• [25] Lim TJ (1998) A stochastic regime switching model for the failure process of a repairable system. Reliability Engrg. System Safety 59(2):225–238.Crossref, Google Scholar
• [26] Lv S (2020) Two-player zero-sum stochastic differential games with regime switching. Automatica 114:108819.Crossref, Google Scholar
• [27] Lv S, Wu Z, Xiong J (2024) Linear quadratic nonzero-sum mean-field stochastic differential games with regime switching. Appl. Math. Optim. 90(2):44.Crossref, Google Scholar
• [28] Lv S, Xiong J, Zhang X (2023) Linear quadratic leader-follower stochastic differential games for mean-field switching diffusions. Automatica 154:111072.Crossref, Google Scholar
• [29] Ma J, Protter PE, Yong J (1994) Solving forward-backward stochastic differential equations explicitly—A four step scheme. Probab. Theory Related Fields 98(3):339–359.Crossref, Google Scholar
• [30] Mei H, Nguyen SL, Yin G (2025) Closed-loop equilibria for mean-field games in randomly switching environments with general discounting costs. SIAM J. Control Optim. 63(2):966–992.Crossref, Google Scholar
• [31] Mei H, Wei Q, Yong J (2024) Linear-quadratic optimal control problem for mean-field stochastic differential equations with a type of random coefficients. Numerical Algebra Control Optim. 14(4):813–852.Crossref, Google Scholar
• [32] Nguyen SL, Yin G, Hoang TA (2020) On laws of large numbers for systems with mean-field interactions and Markovian switching. Stochastic Processes Appl. 130(1):262–296.Crossref, Google Scholar
• [33] Nguyen SL, Yin G, Nguyen DT (2021) A general stochastic maximum principle for mean-field controls with regime switching. Appl. Math. Optim. 84(3):3255–3294.Crossref, Google Scholar
• [34] Pham H (2009) Continuous-Time Stochastic Control and Optimization with Financial Applications, vol. 61 (Springer, Berlin).Crossref, Google Scholar
• [35] Protter PE (1992) Stochastic Integration and Differential Equations, 2nd ed. (Springer, Berlin).Google Scholar
• [36] Rockafellar RT, Wets RJB (2009) Variational Analysis, vol. 317 (Springer, Berlin).Google Scholar
• [37] Rolón Gutiérrez EJ, Nguyen SL, Yin G (2024) Markovian-switching systems: Backward and forward-backward stochastic differential equations, mean-field interactions, and nonzero-sum differential games. Appl. Math. Optim. 89(2):33.Crossref, Google Scholar
• [38] Savku E, Weber GW (2022) Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market. Ann. Oper. Res. 312(2):1171–1196.Crossref, Google Scholar
• [39] Shao J, Wei D (2022) Propagation of chaos and conditional McKean-Vlasov SDEs with regime-switching. Frontiers Math. China 17(4):731–746.Crossref, Google Scholar
• [40] Shao J, Tian T, Wang S (2024) Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: Wellposedness, propagation of chaos, averaging principle. J. Math. Anal. Appl. 534(2):128080.Crossref, Google Scholar
• [41] Song Q, Yin GG, Zhang Z (2008) Numerical solutions for stochastic differential games with regime switching. IEEE Trans. Automatic Control 53(2):509–521.Crossref, Google Scholar
• [42] Yong J, Zhou XY (2012) Stochastic Controls: Hamiltonian Systems and HJB Equations, vol. 43 (Springer, Berlin).Google Scholar
• [43] Zhang Q (2001) Stock trading: An optimal selling rule. SIAM J. Control Optim. 40(1):64–87.Crossref, Google Scholar
• [44] Zhang P, Xu ZQ (2024) Multidimensional indefinite stochastic Riccati equations and zero-sum stochastic linear-quadratic differential games with non-Markovian regime switching. SIAM J. Control Optim. 62(6):3239–3265.Crossref, Google Scholar
• [45] Zhang X, Sun Z, Xiong J (2018) A general stochastic maximum principle for a Markov regime switching jump-diffusion model of mean-field type. SIAM J. Control Optim. 56(4):2563–2592.Crossref, Google Scholar