The maximum principle for a jump-diffusion mean-field model and its application to the mean-variance problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 86, Issue , 2013, Pages 58-73

  Shen, Yang ^a   Siu, Tak Kuen ^a,b  

^a MACQUARIE UNIVERSITY   (Australia)

^b CITY UNIVERSITY   (United Kingdom)

Author keywords

Backward stochastic differential equation; Jump diffusion; Mean field model; Mean variance portfolio selection; Stochastic maximum principle

Indexed keywords

BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; JUMP-DIFFUSION; MEAN FIELD MODELS; MEAN-VARIANCE PORTFOLIOS; STOCHASTIC MAXIMUM PRINCIPLES;

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; DIFFUSION; MAXIMUM PRINCIPLE; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 84876176307     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2013.02.029     Document Type: Article

References (24)

1. H.J. Kushner Conditions for continuous parameter stochastic optimization problems SIAM Journal on Control and Optimization 10 1972 550 565
2. J.M. Bismut Conjugate convex functions in optimal stochastic control Journal of Mathematical Analysis and Applications 44 1973 384 404
3. S. Peng A general stochastic maximum principle for optimal control problems SIAM Journal on Control and Optimization 28 1990 966 979
4. S. Tang, and X. Li Necessary conditions for optimal control of stochastic systems with random jumps SIAM Journal on Control and Optimization 32 1994 1447 1475
5. A. Cadenillas, and I. Karatzas The stochatic maximum principle for linear, convex optimal control with random coefficients SIAM Journal on Control and Optimization 33 1995 590 624
6. N.C. Framstad, B. Øksendal, and A. Sulem Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance Journal of Optimization Theory and Applications 121 2004 77 98
7. T.T.K. An, and B. Øksendal Maximum principle for stochastic differential games with partial information Journal of Optimization Theory and Applications 139 2008 463 483
8. B. Øksendal, and A. Sulem Maximum principles for optimal control of forward-backward stochastic differential equations with jumps SIAM Journal on Control and Optimization 48 2009 2845 2976
9. B. Øksendal, A. Sulem, Forward-backward SDE games and stochastic control under model uncertainty, University of Oslo, 2011, Preprint.
10. A. Bensoussan Lectures on stochastic control S.K. Mitter, A. Moro, Nonlinear Filtering and Stochastic Control Springer Lecture Notes in Mathematics vol. 972 1982 Springer Berlin
11. R.J. Elliott Stochastic Calculus and Applications 1982 Springer-Verlag New York
12. J. Yong, and X.Y. Zhou Stochastic Control: Hamiltonian Systems and HJB Equations 1999 Springer Verlag New York
13. B. Øksendal, and A. Sulem Applied Stochastic Control of Jump Diffusions second ed. 2007 Springer Berlin
14. X. Zhang, R.J. Elliott, and T.K. Siu A stochastic maximum principle for a markov regime-switching jump-diffusion model and its application to finance SIAM Journal on Control and Optimization 50 2012 964 990
15. J.M. Lasry, and P.L. Lions Mean-field games Japanese Journal of Mathematics 2 2007 229 260
16. R. Buckdahn, B. Djehiche, J. Li, and S. Peng Mean-field backward stochastic differential equations: a limit approach Annals of Probability 37 2009 1524 1565
17. R. Buckdahn, J. Li, and S. Peng Mean-field backward stochastic differential equations and related partial differential equations Stochastic Processes and their Applications 119 2009 3133 3154
18. T. Meyer-Brandis, B. Øksendal, X.Y. Zhou, A mean-field stochastic maximum principle via Malliavin calculus, Stochastics, http://dx.doi.org/10. 1080/17442508.2011.651619, 2010.
19. D. Andersson, and B. Djehiche A maximum principle for SDEs of mean-field type Applied Mathematics and Optimization 63 2011 341 356
20. R. Buckdahn, B. Djehiche, and J. Li A general stochastic maximum principle for SDEs of mean-field type Applied Mathematics and Optimization 64 2011 197 216
21. J. Li Stochastic maximum principle in the mean-field controls Automatica 48 2012 366 373
22. O. Guéant, J.M. Lasry, P.L. Lions, Mean-field games and applications, in: A.R. Carmona et al. (Eds.), Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Mathematics 2003, 205-266, 2011.
23. A. Bensoussan, K.C.J. Sung, S.C.P. Yam, S.P. Yung, Linear-quadratic mean-field games, The Chinese University of Hong Kong, 2011, Preprint.
24. X.Y. Zhou, and D. Li Continuous-time mean-variance portfolio selection: a stochastic LQ framework Applied Mathematics and Optimization 42 2000 19 33