Y. Ait-sahalia, J. Fan, and D. Xiu, High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data, Journal of the American Statistical Association, vol.105, issue.492, pp.1504-1517, 2010.
DOI : 10.1198/jasa.2010.tm10163

D. Andersson and B. Djehiche, A Maximum Principle for SDEs of Mean-Field Type, Applied Mathematics & Optimization, vol.42, issue.7, pp.341-356, 2011.
DOI : 10.1007/s00245-010-9123-8

M. Avellaneda, A. Levy, and A. Paras, Pricing and hedging derivative securities in markets with uncertain volatilities, Applied Mathematical Finance, vol.7, issue.2, pp.73-88, 1995.
DOI : 10.2307/2330793

A. Bensoussan, J. Frehse, and P. Yam, The Master equation in mean field theory, Journal de Math??matiques Pures et Appliqu??es, vol.103, issue.6, pp.1441-1474, 2015.
DOI : 10.1016/j.matpur.2014.11.005

R. Buckdahn, J. Li, S. Peng, and C. Rainer, Mean-field stochastic differential equations and associated PDEs, The Annals of Probability, vol.45, issue.2, 2014.
DOI : 10.1214/15-AOP1076
URL : http://arxiv.org/abs/1407.1215

P. Cardaliaguet, Notes on mean field games, Notes from P.L. Lions lectures at Collège de France, 2012.

J. F. Chassagneux, D. Crisan, and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01144845

M. C. Chiu and H. Y. Wong, Mean???variance portfolio selection with correlation risk, Journal of Computational and Applied Mathematics, vol.263, pp.432-444, 2014.
DOI : 10.1016/j.cam.2013.12.050

G. Deelstra and F. Delbaen, Convergence of discretized stochastic (interest rate) processes with stochastic drift term, Applied Stochastic Models and Data Analysis, vol.14, issue.1, pp.77-84, 1998.
DOI : 10.1002/(SICI)1099-0747(199803)14:1<77::AID-ASM338>3.0.CO;2-2

L. Denis and C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, The Annals of Applied Probability, vol.16, issue.2, pp.827-852, 2006.
DOI : 10.1214/105051606000000169

L. G. Epstein and S. Ji, Ambiguous Volatility and Asset Pricing in Continuous Time, Review of Financial Studies, vol.26, issue.7, pp.1740-1786, 2013.
DOI : 10.1093/rfs/hht018
URL : http://arxiv.org/abs/1301.4614

F. Fabozzi, D. Huang, and G. Zhou, Robust portfolios: contributions from operations research and finance, Annals of Operations Research, vol.34, issue.3, pp.191-220, 2010.
DOI : 10.1007/s10479-009-0515-6
URL : http://apps.olin.wustl.edu/faculty/zhou/FHZ_10.pdf

M. Fisher and G. Livieri, Continuous time mean-variance portfolio optimization through the mean field approach, ESAIM: Probability and Statistics, vol.20, 2015.
DOI : 10.1051/ps/2016001

J. P. Fouque, C. S. Pun, and H. Y. Wong, Portfolio optimization with ambiguous correlation and stochastic volatilities, 2015.
DOI : 10.2139/ssrn.2479796

L. P. Hansen and T. J. Sargent, Robust Control and Model Uncertainty, American Economic Review, vol.91, issue.2, pp.60-66, 2001.
DOI : 10.1257/aer.91.2.60

T. Hayashi and N. Yoshida, On covariance estimation of non-synchronously observed diffusion processes, Bernoulli, vol.11, issue.2, pp.359-379, 2005.
DOI : 10.3150/bj/1116340299

A. Ismail and H. Pham, Robust Markowitz mean-variance portfolio selection under ambiguous volatility and correlation, 2016.

R. Jagannathan and T. Ma, Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps, The Journal of Finance, vol.9, issue.4, pp.1651-1684, 2003.
DOI : 10.1111/1540-6261.00580

B. Jourdain, S. Méléard, and W. A. Woyczynski, Nonlinear SDEs driven by Lévy processes and related PDEs, ALEA Lat. Am. J. Probab. Math. Stat, vol.4, pp.1-29, 2008.

H. Q. Jin and X. Y. Zhou, Continuous-time portfolio selection under ambiguity, Mathematical Control and Related Fields, vol.5, issue.3, pp.475-488, 2015.
DOI : 10.3934/mcrf.2015.5.475

R. Karandikar, On pathwise stochastic integration, Stochastic Processes and their Applications, pp.11-18, 1995.
DOI : 10.1016/0304-4149(95)00002-O
URL : http://doi.org/10.1016/0304-4149(95)00002-o

Q. Lin and F. Riedel, Optimal consumption and portfolio choice with ambiguity Correlation ambiguity, 2014.
DOI : 10.2139/ssrn.2377452
URL : http://arxiv.org/abs/1401.1639

T. Lyons, Uncertain volatility and the risk-free synthesis of derivatives, Applied Mathematical Finance, vol.20, issue.2, pp.117-133, 1995.
DOI : 10.1002/cpa.3160450103

H. Markowitz, PORTFOLIO SELECTION*, The Journal of Finance, vol.7, issue.1, pp.77-91, 1952.
DOI : 10.1111/j.1540-6261.1952.tb01525.x

A. Matoussi, D. Possamaï, and C. Zhou, ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL, Mathematical Finance, vol.32, issue.1, pp.258-287, 2015.
DOI : 10.1111/mafi.12031
URL : https://hal.archives-ouvertes.fr/hal-00919124

M. Nutz, Pathwise construction of stochastic integrals, Electronic Communications in Probability, vol.17, issue.0, pp.1-7, 2012.
DOI : 10.1214/ECP.v17-2099

S. Peng, G-Expectation, G-Brownian Motion and Related Stochastic Calculus of It?? Type, The Abel Symposium 2005, Abel Symposia 2, pp.541-567, 2006.
DOI : 10.1007/978-3-540-70847-6_25

H. Pham and X. Wei, Dynamic programming for optimal control of stochastic McKean- Vlasov dynamics, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01302289

M. Pinar, On robust mean-variance portfolios, Optimization, vol.48, issue.5, pp.1039-1048, 2016.
DOI : 10.1111/1467-9965.00100

R. Rebonato and P. Jäckel, The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes, SSRN Electronic Journal, vol.19, pp.1767-1768, 1999.
DOI : 10.2139/ssrn.1969689

T. Rockafellar, Convex analysis, 1970.
DOI : 10.1515/9781400873173

A. S. Sznitman, Topics in propagation of chaos, Lecture Notes in Mathematics, vol.22, issue.1, pp.165-251, 1989.
DOI : 10.1070/SM1974v022n01ABEH001689

H. M. Soner, N. Touzi, and J. Zhang, Quasi-sure Stochastic Analysis through Aggregation, Electronic Journal of Probability, vol.16, issue.0, pp.1844-1879, 2011.
DOI : 10.1214/EJP.v16-950
URL : http://arxiv.org/abs/1003.4431

H. M. Soner, N. Touzi, and J. Zhang, Wellposedness of second order BSDEs, Probability Theory and Related Fields, pp.149-190, 2012.

D. Wagner, Survey of measurable selection theorems: An update, Lect. Notes in Math, vol.59, 1980.
DOI : 10.2140/pjm.1975.59.267

X. Y. Zhou and D. Li, Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework, Applied Mathematics and Optimization, vol.42, issue.1, pp.19-33, 2000.
DOI : 10.1007/s002450010003