A maximum principle for SDEs of mean-field type

Applied Mathematics and Optimization

Volumn 63, Issue 3, 2011, Pages 341-356

  Andersson, Daniel ^a   Djehiche, Boualem ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Maximum principle; McKean Vlasov equation; Mean field SDE; Stochastic control; Time inconsistent control

Indexed keywords

ACTION SPACES; ADJOINT EQUATIONS; CONTROL PROBLEMS; COST FUNCTIONALS; MCKEAN-VLASOV EQUATION; MEAN VARIANCE; MEAN-FIELD; MEAN-FIELD SDE; OPTIMAL CONTROLS; OPTIMALITY; OPTIMALITY PRINCIPLE; PORTFOLIO SELECTION PROBLEMS; STOCHASTIC CONTROL; STOCHASTIC DIFFERENTIAL EQUATIONS; TIME INCONSISTENT CONTROL;

DIFFERENTIAL EQUATIONS; STOCHASTIC SYSTEMS;

MAXIMUM PRINCIPLE;

EID: 79958262462     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-010-9123-8     Document Type: Article

References (15)

1. Ahmed, N.U., Ding, X.: Controlled McKean-Vlasov equations. Commun. Appl. Anal. 5(2), 183-206 (2001). (Pubitemid 33286366)
2. Basak, S., Chabakauri, G.: Dynamic mean-variance asset allocation. In: EFA 2007 Ljubljana Meetings; AFA 2009 San Francisco Meetings Paper. SSRN: http://ssrn.com/abstract=965926 (2009).
3. Bensoussan, A.: Lectures on stochastic control. In: Mitter, S.K., Moro, A. (eds.) Nonlinear Filtering and Stochastic Control. Springer Lecture Notes in Mathematics, vol. 972. Springer, Berlin (1982).
4. Björk, T., Murgoci, A.: A general theory of Markovian time inconsistent stochastic control problems. Preprint (2008).
5. Buckdahn, R., Li, J., Peng, S.: Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Process. Appl. 119(10), 3133-3154 (2007).
6. Buckdahn, R., Djehiche, B., Li, J., Peng, S.: Mean-field backward stochastic differential equations. A limit approach. Ann. Probab. 37(4), 1524-1565 (2009).
7. Chighoub, F., Djehiche, B., Mezerdi, B.: The stochastic maximum principle in optimal control of degenerate diffusions with non-smooth coefficients. Random Oper. Stoch. Equ. 17, 35-53 (2008).
8. Framstad, N.C., Sulem, A., Øksendal, B.: Sufficient stochastic maximum principle for optimal control of jump diffusions and applications to finance. J. Optim. Theory Appl. 121(1), 77-98 (2004). (Pubitemid 39064410)
9. Huang, M., Malhamé, R.P., Caines, P.E.: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6(3), 221- 252 (2006).
10. Jourdain, B., Méléard, S., Woyczynski, W.: Nonlinear SDEs driven by Lévy processes and related PDEs. Alea 4, 1-29 (2008).
11. Kantorovich, L.B., Rubinstein, G.S.: On the space of completely additive functions. Vestn. Leningr. Univ., Mat. Meh. Astron. 13(7), 52-59 (1958).
12. Lasry, J.M., Lions, P.L.: Mean-field games. Jpn. J. Math. 2, 229-260 (2007).
13. Sznitman, A.S.: Topics in propagation of chaos. In: Ecôle de Probabilites de Saint Flour, XIX-1989. Lecture Notes in Math, vol. 1464, pp. 165-251. Springer, Berlin (1989).
14. Yong, J., Zhou, X.Y.: Stochastic Control: Hamiltonian Systems and HJB Equations. Springer, New York (1999).
15. Zhou, X.Y., Li, D.: Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42, 19-33 (2000).