Sufficient Stochastic Maximum Principle for Discounted Control Problem

Applied Mathematics and Optimization

Volumn 70, Issue 2, 2014, Pages 225-252

  Maslowski, Bohdan ^a   Veverka, Petr ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Discounted control problem; FBSDE; Infinite horizon; Stochastic logistic equation; Stochastic maximum principle

Indexed keywords

EQUATIONS OF STATE; HAMILTONIANS; MAXIMUM PRINCIPLE; STOCHASTIC CONTROL SYSTEMS;

CONTROL PROBLEMS; FBSDE; INFINITE HORIZONS; LOGISTIC EQUATIONS; STOCHASTIC MAXIMUM PRINCIPLES;

STOCHASTIC SYSTEMS;

EID: 84939415091     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-014-9241-9     Document Type: Article

References (32)

1. Agram N., Haadem S., Øksendal B., Proske F.: A maximum principle for infinite horizon delay equations (2013). doi:10.1137/120882809
2. Al-Hussein, A.: Maximum principle for controlled stochastic evolution equations. Int. J. Math. Anal. 4, 1447–1464 (2010)
3. Bahlali, S., Mezerdi, B.: A general stochastic maximum principle for singular control problems. Elect. J. Probab. 10, 988–1004 (2005)
4. Bensoussan, A.: Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Stochastics 9, 169–222 (1983)
5. Bismut, J.-M.: Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44, 384–404 (1973)
6. Borkar, V.S.: Controlled diffusion processes. Probab. Surv. 2, 213–244 (2005)
7. Cadenillas, A., Haussman, U.: The stochastic maximum principle for singular control problem. Stochastics 49(3–4), 211–237 (1994)
8. Chikodza, E.: Combined singular and impulse control for jump diffusions. SAMSA J. Pure Appl. Math. 3, 29–57 (2008)
9. Darling, R.W.R., Pardoux, E.: Backward SDE with random terminal time and applications to semilinear elliptic PDE. Ann. Probab. 25(3), 1135–1159 (1997)
10. Dufour, F., Miller, B.: Maximum principle for singular stochastic control problems. SIAM J. Control Optim. 45(2), 668–698 (2006)
11. Framstad, N.C., Øksendal, B., Sulem, A.: Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance. J. Optim. Theo. Appl. 121, 77–98 (2004); Erratum: J. Optim. Theo. Appl. 124, 511–512, (2005)
12. Friedman, A.: Stochastic Differential Equations and Applications. Academic Press, New York (1975)
13. Fuhrman, M., Hu, Y., Tessitore, G.: Stochastic maximum principle for optimal control of SPDEs. Comptes Rendus Math. 350, 683–688 (2012)
14. Gabasov, R., Kirillova, M., Mordukhovich, B.S.: The $$\varepsilon $$ε—maximum principle for suboptimal controls. Soviet Math. Dokh. 27, 95–99 (1983)
15. Haadem, S., Øksendal, B., Proske, F.: Maximum principles for jump diffusion processes with infinite horizon. Automatica 49(7), 2267–2275 (2013)
16. Ikeda, N., Watanabe, S.: A comparison theorem for solutions of stochastic differential equations and its applications. Osaka J. Math. 14, 619–633 (1977)
17. Kushner, H.J.: Necessary conditions for continuous parameter stochastic optimization problems. SIAM J. Control Optim. 10, 550–565 (1972)
18. Stochastic, Øksendal B., Equations, Differential: An Introduction with Applications, 4th edn. Springer-Verlag (Universitext), Berlin (1995)
19. Øksendal, B., Sulem, A.: Singular stochastic control and optimal stopping with partial information of Itô-Lévy processes. SIAM J. Control Optim. 50, 2254–2287 (2012)
20. Øksendal, B., Sulem, A., Zhang, T.: Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations. Int. Adv. Appl. Probab. 43, 572–596 (2011)
21. Pardoux, E.: BSDEs weak convergence and homogenizations of semilinear PDEs. In: Clark, F.H., Stern, R.J. (eds.) Nonlinear Analysis Differential Equations and Control, pp. 503–509. Kluwer Academic, Dordrecht (1999)
22. Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14, 55–61 (1990)
23. Peng, S.: A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28, 966–979 (1990)
24. Peng, S., Shi, Y.: Infinite horizon forward–backward stochastic differential equations. Stochastic Process. Appl. 85, 75–92 (2000)
25. Peng, S., Wu, Z.: Fully coupled forward backward stochastic differential equations and application to optimal control. SIAM J. Control Optim. 37(3), 825–843 (1999)
26. Pham, H.: Continuous-time Stochastic Control and Optimization with Financial Applications. Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2009)
27. Tang, S.J., Li, X.J.: Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Control Optim. 32, 1447–1475 (1994)
28. Wu, Z.: Forward–backward stochastic differential equations with stopping time. Acta Math. Sci. 24, 91–99 (2004)
29. Wu, Z., Zhang, F.: Maximum principle for stochastic recursive optimal control problems involving impulse controls. Abstr. Appl. Anal. 32, 1–16 (2012)
30. Yin, J.: On solutions of a class of infinite horizon FBSDE’s. Stat. Probab. Lett. 78, 2412–2419 (2008)
31. Yong, J., Zhou, X.Y.: Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999)
32. Zhou, X.Y.: Stochastic near-optimal controls. Necessary and sufficient conditions for near-optimality. SIAM J. Control Optim. 36, 929–947 (1998)