Chinese Annals of Mathematics,Series B, Volume. 46, Issue 4, 521(2025)

Ergodic Stochastic Maximum Principle with Markov Regime-Switching

WU Zhen and ZHANG Honghao
References(25)

[1] [1] Arisawa, M. and Lions, P. L., On ergodic stochastic control,Communications in Partial Differential Equations,23, 1998, 2187–2217.

[2] [2] Bellalah, M., Hakim, A., Si, K. and Zhang, D., Long term optimal investment with regime switching: Inflation, information and short sales,Annals of Operations Research,313, 2022, 1373–1386.

[3] [3] Benabdallah, H., Tamer, L. and Chaouchkhouane, N., Stochastic maximum principle for a Markov regime switching jump-diffusion in infinite horizon,International Journal of Nonlinear Analysis and Applications,13(2), 2022, 1477–1494.

[4] [4] Bensoussan, A. and Frehse, J., On Bellman equations of ergodic control in Rn, Applied Stochastic Analysis (eds. I. Karatzas and D. Ocone),177, Springer-Verlag, Berlin, Heidelberg, 1992, 21–29.

[5] [5] Bismut, J. M., An introductory approach to duality in optimal stochastic control,SIAM Review,20, 1978, 62–78.

[6] [6] Briand, Ph., Delyon, B., Hu, Y., et al., Lp solutions of backward stochastic differential equations,Stochastic Processes and their Applications,108, 2003, 109–129.

[7] [7] Cerrai, S., Second Order PDE's in Finite and Infinite Dimension,1762, Lecture Notes in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2001.

[8] [8] Donnelly, C., Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model,Applied Mathematics Optimization,64, 2011, 155–169.

[9] [9] Fuhrman, M., Hu, Y. and Tessitore, G., Ergodic BSDEs and optimal ergodic control in Banach spaces,SIAM Journal on Control and Optimization,48, 2009, 1542–1566.

[10] [10] Ghosh, M. K., Arapostathis, A. and Marcus, S. I., Ergodic control of switching diffusions,SIAM Journal on Control and Optimization,35, 1997, 1952–1988.

[11] [11] Hamilton, J. D., A new approach to the economic analysis of nonstationary time series and the business cycle,Econometrica,57, 1989, 357.

[12] [12] Huang, Y. T., Song, Q. and Zheng, H., Weak convergence of path-dependent SDEs in basket credit default swap pricing with contagion risk,SIAM Journal on Financial Mathematics,8, 2017, 1–27.

[13] [13] Kushner, H. J., Necessary conditions for continuous parameter stochastic optimization problems,SIAM Journal on Control,10, 1972, 550–565.

[14] [14] Orrieri, C., Tessitore, G. and Veverka, P., Ergodic maximum principle for stochastic systems,Applied Mathematics Optimization,79, 2019, 567–591.

[15] [15] Orrieri, C. and Veverka, P., Necessary stochastic maximum principle for dissipative systems on infinite time horizon,ESAIM: Control, Optimisation and Calculus of Variations,23, 2017, 337–371.

[16] [16] Pardoux, E., BSDEs, weak convergence and homogenization of semilinear PDEs, Nonlinear Analysis, Differential Equations and Control, Clarke, F. H., Stern, R. J. and Sabidussi, G.,(eds.), Springer Netherlands, Dordrecht, 1999, 503–549.

[17] [17] Pardoux, E. and Peng, S., Adapted solution of a backward stochastic differential equation,Systems Control Letters,14, 1990, 55–61.

[18] [18] Peng, S., A general stochastic maximum principle for optimal control problems,SIAM Journal on Control and Optimization,28, 1990, 966–979.

[19] [19] Rogers, L. C. G. and Williams, D., Diffusions, Markov Processes and Martingales, vol.1, 2nd edition, Cambridge University Press, Cambrdge, 2000.

[20] [20] Tao, R. and Wu, Z., Maximum principle for optimal control problems of forward-backward regime-switching system and applications,Systems Control Letters,61, 2012, 911–917.

[21] [21] Wang, S. and Wu, Z., Maximum principle for optimal control problems of forward-backward regime-switching systems involving impulse controls,Mathematical Problems in Engineering,2015, 2015, 1–13.

[22] [22] Yang, D., Li, X. and Qiu, J., Output tracking control of delayed switched systems via state dependent switching and dynamic output feedback,Nonlinear Analysis: Hybrid Systems,32, 2019, 294–305.

[23] [23] Yang, D., Li, X., Shen, J. and Zhou, Z., State-dependent switching control of delayed switched systems with stable and unstable modes,Mathematical Methods in the Applied Sciences,41, 2018, 6968–6983.

[24] [24] Zhang, X., Sun, Z. and Xiong, J., A general stochastic maximum principle for a Markov regime switching jump-diffusion model of mean-field type,SIAM Journal on Control and Optimization,56, 2018, 2563–2592.

[25] [25] Zhou, X. Y. and Yin, G., Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model,SIAM Journal on Control and Optimization,42, 2003, 1466–1482.

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WU Zhen, ZHANG Honghao. Ergodic Stochastic Maximum Principle with Markov Regime-Switching[J]. Chinese Annals of Mathematics,Series B, 2025, 46(4): 521

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Paper Information

Received: May. 1, 2024

Accepted: Aug. 25, 2025

Published Online: Aug. 25, 2025

The Author Email:

DOI:10.1007/s11401-025-0027-y

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