Global maximum principle for the forward-backward stochastic optimal control problem with poisson jumps

Asian Journal of Control

Volumn 14, Issue 5, 2012, Pages 1355-1365

  Shi, Jingtao ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Clarke generalized gradient; forward backward stochastic system; maximum principle; Poisson jumps; Stochastic optimal control

Indexed keywords

GLOBAL OPTIMIZATION; MAXIMUM PRINCIPLE; OPTIMAL CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CONTROL DOMAINS; CONTROL VARIABLE; GENERALIZED GRADIENTS; OPTIMALITY; POISSON JUMPS; STATE CONSTRAINTS; STOCHASTIC OPTIMAL CONTROL; STOCHASTIC OPTIMAL CONTROL PROBLEM;

STOCHASTIC CONTROL SYSTEMS;

EID: 84866725410     PISSN: 15618625     EISSN: 19346093     Source Type: Journal    
DOI: 10.1002/asjc.443     Document Type: Article

References (19)

1. Yong, J. M., and, X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, NY, U.S.A. (1999).
2. Pardoux, E., and, S. G. Peng, " Adapted solution of a backward stochastic differential equation," Syst. Control Lett., Vol. 14, pp. 55-61 (1990). (Pubitemid 20649275)
3. El Karoui, N., S. G. Peng, and, M. C. Quenez, " Backward stochastic differential equations in finance," Math. Financ., Vol. 7, No. 1, pp. 1-71 (1997). (Pubitemid 127342795)
4. Peng, S. G., " Backward stochastic differential equations and applications to optimal control," Appl. Math. Optim., Vol. 27, pp. 125-144 (1993).
5. Xu, W. S., " Stochastic maximum principle for optimal control problem of forward and backward system," J. Aus. Math. Soc. B, Vol. 37, pp. 172-185 (1995).
6. Wang, G. C., and, Z. Wu, " The maximum principles for stochastic recursive optimal control problems under partial information," IEEE Trans. Autom. Control, Vol. 54, No. 6, pp. 1230-1242 (2009).
7. Wu, Z., " A general maximum principle for optimal control problems of forward-backward stochastic control systems," in press.
8. Wu, Z., " A maximum principle for partially observed optimal control of forward-backward stochastic control systems," Sci. China Ser F-Inf. Sci., Vol. 53, No. 11, pp. 2205-2214 (2010).
9. Merton, R. C., " Option pricing when underlying stock returns are dis-continuous," J. Financ. Econ., Vol. 2, pp. 125-144 (1976).
10. Cont, R., and, P. Tankov, Financial Modelling with Jump Processes, Chapman & Hall/CRC, New York, NY, U.S.A. (2004).
11. Situ, R., " A maximum principle for optimal controls of stochastic systems with random jumps," Proc. Nat. Conf. Control Theory Appl., Qingdao, P. R. China (1991).
12. Tang, S. J., and, X. J. Li, " Necessary conditions for optimal control of stochastic systems with random jumps," SIAM J. Control Optim., Vol. 32, No. 5, pp. 1447-1475 (1994).
13. Framstad, N. C., B. Oksendal, and, A. Sulem, " A sufficient stochastic maximum principle for optimal control of jump diffusions and applications to finance," J. Optim. Theory Appl., Vol. 121, No. 1, pp. 77-98 (2004) (errata, Vol. 124, No. 2, pp. 511-512 (2005)). (Pubitemid 39064410)
14. Shi, J. T., and, Z. Wu, " Maximum principle for forward-backward stochastic control systems with random jumps and applications to finance," J. Syst. Sci. Complex, Vol. 23, pp. 219-231 (2010).
15. Oksendal, B., and, A. Sulem, " Maximum principles for optimal control of forward-backward stochastic differential equations with jumps," SIAM J. Control Optim., Vol. 48, No. 5, pp. 2945-2976 (2009).
16. Zhou, X. Y., " Sufficient conditions of optimality for stochastic systems with controllable diffusions," IEEE Trans. Autom. Control, Vol. 41, No. 8, pp. 1176-1179 (1996). (Pubitemid 126767953)
17. Docuchaev, N., and, X. Y. Zhou, " Stochastic controls with terminal contingent conditions," J. Math. Anal. Appl., Vol. 238, pp. 143-165 (1999).
18. Ikeda, N., and, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland and Kodansha, Amsterdam, Netherlands and Tokyo, Japan (1989).
19. Wu, Z., " Forward-backward stochastic differential equations with Brownian motion and Poisson process," ACTA Math. Appl. Sin., Vol. 15, No. 4, pp. 433-443 (1999).