A. B. Abel, Asset prices under habit formation and catching up with the Joneses, American Economic Review, vol.80, pp.38-42, 1990.
DOI : 10.3386/w3279

M. Akian, J. Menaldi, and A. Sulem, Multi-asset portfolio selection problem with transaction costs, Probabilités numériques, pp.163-172, 1992.
DOI : 10.1016/0378-4754(93)E0079-K

I. B. Tahar, H. M. Soner, and N. Touzi, Modelling continuous-time financial markets with capital gains taxes, 2008.

I. B. Tahar, H. M. Soner, and N. Touzi, The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes, SIAM Journal on Control and Optimization, vol.46, issue.5, pp.1779-1801, 2008.
DOI : 10.1137/050646044

URL : https://hal.archives-ouvertes.fr/hal-00703103

D. P. Bertsekas and S. Shreve, Stochastic Optimal Control: the Discrete Time Case, 1978.

J. Bismut, Conjugate convex functions in optimal stochastic control, Journal of Mathematical Analysis and Applications, vol.44, issue.2, pp.384-404, 1973.
DOI : 10.1016/0022-247X(73)90066-8

P. Briand and Y. Hu, Quadratic BSDEs with convex generators and unbounded terminal value. Probab. Theory Relat, pp.543-567, 2008.

G. M. Constantinides, Capital Market Equilibrium with Personal Tax, Econometrica, vol.51, issue.3, pp.611-636, 1983.
DOI : 10.2307/1912150

G. M. Constantinides and M. J. , Portfolio selection with transaction costs, J. Econ. Theory, vol.13, pp.245-263, 1976.

J. Cox and C. F. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory, vol.49, issue.1, pp.33-83, 1989.
DOI : 10.1016/0022-0531(89)90067-7

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

J. Cvitanic and I. Karatzas, Convex Duality in Constrained Portfolio Optimization, The Annals of Applied Probability, vol.2, issue.4, pp.767-818, 1992.
DOI : 10.1214/aoap/1177005576

R. M. Damon, C. S. Spatt, and H. H. Zhang, Optimal Consumption and Investment with Capital Gains Taxes, Review of Financial Studies, vol.14, issue.3, pp.583-616, 2001.
DOI : 10.1093/rfs/14.3.583

G. Da-prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, 1992.

M. H. Davis and A. R. Norman, Portfolio Selection with Transaction Costs, Mathematics of Operations Research, vol.15, issue.4, pp.676-713, 1990.
DOI : 10.1287/moor.15.4.676

P. Demarzo, R. Kaniel, and I. Kremer, Relative wealth concerns and financial bubbles, Rev. Financ. Stud, 2007.

D. Duffie and T. Sun, Transactions costs and portfolio choice in a discrete-continuous-time setting, Journal of Economic Dynamics and Control, vol.14, issue.1, pp.35-51, 1990.
DOI : 10.1016/0165-1889(90)90004-Z

J. , D. Toit, and G. Peskir, The trap of complacency in predicting the maximum, Ann. Probab, vol.35, pp.340-365, 2007.

J. , D. Toit, and G. Peskir, Predicting the time of the ultimate maximum for Brownian motion with drift, Proc. Math. Control Theory Finance, pp.95-112, 2007.

P. Dybvig and H. Koo, Investment with taxes. Working paper, 1996.

R. Elie, Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach, Applied Mathematics and Optimization, vol.32, issue.1, pp.411-431, 2008.
DOI : 10.1007/s00245-008-9044-y

URL : https://hal.archives-ouvertes.fr/hal-00362305

R. Elie and N. Touzi, Optimal lifetime consumption and investment under a??drawdown constraint, Finance and Stochastics, vol.4, issue.3, pp.299-330, 2008.
DOI : 10.1007/s00780-008-0066-8

URL : https://hal.archives-ouvertes.fr/hal-00362302

N. Karoui, Les aspects probabilistes du contrôle stochastique. Ecole d'Eté de Probabilités de Saint-Flour 1979, Lectures notes in Math, pp.73-238, 1981.

N. Karoui, M. Jeanblanc, and V. Lacoste, Optimal portfolio management with American capital guarantee, Journal of Economic Dynamics and Control, vol.29, issue.3, pp.409-440, 2005.
DOI : 10.1016/j.jedc.2003.11.005

N. Karoui, D. Hu-nguyen, and M. Jeanblanc-piqué, Compactification methods in the control of degenerate diffusions: existence of an optimal control, Stochastics, vol.20, pp.169-219, 1987.

N. Karoui, S. Peng, and M. Quenez, Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997.
DOI : 10.1111/1467-9965.00022

N. Karoui and R. Rouge, Pricing via utility maximization and entropy, Math. Finance, vol.10, pp.259-276, 2000.

G. Espinosa, Optimal investment-consumption with taxes: first order expansion for general utility functions, 2010.

G. Espinosa, Optimal investment under relative performance concerns with local risk penalization, 2010.

G. Espinosa and N. Touzi, Detecting the maximum of a mean-reverting scalar process, 2010.

G. Espinosa and N. Touzi, OPTIMAL INVESTMENT UNDER RELATIVE PERFORMANCE CONCERNS, Mathematical Finance, vol.32, issue.1, 2010.
DOI : 10.1111/mafi.12034

C. Frei and G. Reis, Existence issues for multidimensional BSDEs and their relation to finance, 2010.

M. Fuhrman and Y. Hu, Backward Stochastic Differential Equations in Infinite Dimensions with Continuous Driver and Applications, Applied Mathematics and Optimization, vol.56, issue.2, pp.265-302, 2007.
DOI : 10.1007/s00245-007-0897-2

URL : https://hal.archives-ouvertes.fr/hal-00364758

J. Gali, Keeping up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices, Journal of Money, Credit and Banking, vol.26, issue.1, pp.1-8, 1994.
DOI : 10.2307/2078030

M. Gallmeyer, R. Kaniel, and S. Tompaidis, Tax management strategies with multiple risky assets, Journal of Financial Economics, vol.80, issue.2, pp.243-291, 2006.
DOI : 10.1016/j.jfineco.2004.08.010

J. P. Gomez, R. Priestley, and F. Zapatero, The impact of keeping up with the Joneses behavior on asset prices and portfolio choice, Finance Research Letters, vol.4, issue.2, pp.95-103, 2007.
DOI : 10.1016/j.frl.2007.01.002

S. E. Graversen, G. Peskir, and A. N. Shiryaev, Stopping Brownian motion without anticipation as close as possible to its ultimate maximum, Theory Probab. Appl, vol.45, pp.125-136, 2001.

S. Hamadene, Equations stochastiques rétrogrades: le cas localement lipschitzien . Annales de l'IHP, Probabilités et Statistiques, vol.32, issue.5, pp.645-659, 1996.

H. He and N. D. Pearson, Consumption and Portfolio Policies With Incomplete Markets and Short-Sale Constraints: the Finite-Dimensional Case, Mathematical Finance, vol.11, issue.3, pp.1-10, 1991.
DOI : 10.1137/0325086

H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case, Journal of Economic Theory, vol.54, issue.2, pp.259-304, 1991.
DOI : 10.1016/0022-0531(91)90123-L

D. Hobson, Optimal stopping of the maximum process: a converse to the results of Peskir, Stochastics An International Journal of Probability and Stochastic Processes, vol.2, issue.1-2, pp.85-102, 2007.
DOI : 10.1112/blms/21.4.305

Y. Hu, P. Imkeller, and M. Müller, Utility maximization in incomplete markets, The Annals of Applied Probability, vol.15, issue.3, pp.1691-1712, 2005.
DOI : 10.1214/105051605000000188

Y. Hu and S. Peng, On the comparison theorem for multidimensional BSDEs, Comptes Rendus Mathematique, vol.343, issue.2, pp.135-140, 2006.
DOI : 10.1016/j.crma.2006.05.019

URL : https://hal.archives-ouvertes.fr/hal-00451661

E. Jouini, P. Koehl, and N. Touzi, Optimal investment with taxes: an optimal control problem with endogeneous delay, Nonlinear Analysis: Theory, Methods & Applications, vol.37, issue.1, pp.31-56, 1997.
DOI : 10.1016/S0362-546X(98)00139-4

URL : https://hal.archives-ouvertes.fr/halshs-00167141

E. Jouini, P. Koehl, and N. Touzi, Optimal investment with taxes: an existence result, Journal of Mathematical Economics, vol.33, issue.4, pp.373-388, 1999.
DOI : 10.1016/S0304-4068(99)00034-8

URL : https://hal.archives-ouvertes.fr/halshs-00167145

I. Karatzas, J. P. Lehoczky, and S. E. Shreve, Optimal Portfolio and Consumption Decisions for a ???Small Investor??? on a Finite Horizon, SIAM Journal on Control and Optimization, vol.25, issue.6, pp.1557-1586, 1987.
DOI : 10.1137/0325086

I. Karatzas, J. P. Lehoczky, S. E. Shreve, and G. Xu, Martingale and Duality Methods for Utility Maximization in an Incomplete Market, SIAM Journal on Control and Optimization, vol.29, issue.3, pp.702-730, 1991.
DOI : 10.1137/0329039

I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 1991.
DOI : 10.1007/978-1-4612-0949-2

I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, 1998.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, 1981.

N. Kazamaki, Continuous Exponential Martingales and BMO. Lecture notes in Math, 1994.

M. Kobylanski, differential equations with quadratic growth, The Annals of Probability, vol.28, issue.2, pp.558-602, 2000.
DOI : 10.1214/aop/1019160253

D. Kramkov and W. Schachermayer, The condition on the asymptotic elasticity of utility functions and optimal investment in incomplete markets, Ann. Appl. Probab, vol.9, pp.904-950, 1999.

D. Kramkov and W. Schachermayer, Necessary and sufficient conditions in the problem of optimal investment in incomplete markets, Ann. Appl. Probab, vol.13, issue.4, pp.1504-1516, 2003.

D. Kramkov and M. Sirbu, On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets, The Annals of Applied Probability, vol.16, issue.3, pp.1352-1384, 2006.
DOI : 10.1214/105051606000000259

J. Lasry and P. Lions, Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007.
DOI : 10.1007/s11537-007-0657-8

URL : https://hal.archives-ouvertes.fr/hal-00667356

T. Lim and M. Quenez, Utility maximization in incomplete markets with default, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00342531

R. C. Merton, Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, The Review of Economics and Statistics, vol.51, issue.3, pp.247-257, 1969.
DOI : 10.2307/1926560

R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, vol.3, issue.4, pp.373-413, 1971.
DOI : 10.1016/0022-0531(71)90038-X

M. Morlais, Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem, Finance and Stochastics, vol.5, issue.1, pp.121-150, 2009.
DOI : 10.1007/s00780-008-0079-3

R. Myneni, The Pricing of the American Option, The Annals of Applied Probability, vol.2, issue.1, pp.1-23, 1992.
DOI : 10.1214/aoap/1177005768

J. Obloj, The Maximality Principle Revisited: On Certain Optimal Stopping Problems, Lect. Notes in Math, vol.1899, pp.309-328, 2007.
DOI : 10.1007/978-3-540-71189-6_16

URL : https://hal.archives-ouvertes.fr/hal-00168854

E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, vol.14, issue.1, pp.55-61, 1990.
DOI : 10.1016/0167-6911(90)90082-6

J. L. Pedersen, Optimal prediction of the ultimate maximum of Brownian motion, Stochastics An International Journal of Probability and Stochastic Processes, vol.75, issue.4, pp.205-219, 2003.
DOI : 10.1080/1045112031000118994

G. Peskir, principle, The Annals of Probability, vol.26, issue.4, pp.1614-1640, 1998.
DOI : 10.1214/aop/1022855875

G. Peskir and A. N. Shiryaev, Optimal Stopping and Free-Boundary Problems, Lectures in Mathematics, 2006.

S. R. Pliska, A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios, Mathematics of Operations Research, vol.11, issue.2, pp.371-382, 1986.
DOI : 10.1287/moor.11.2.371

R. T. Rockafellar, Convex Analysis, 1996.
DOI : 10.1515/9781400873173

L. A. Shepp and A. N. Shiryaev, The Russian Option: Reduced Regret, The Annals of Applied Probability, vol.3, issue.3, pp.631-640, 1993.
DOI : 10.1214/aoap/1177005355

L. A. Shepp and A. N. Shiryaev, A new look at the Russian option. Theory Probab, Appl, vol.39, pp.103-119, 1994.

A. N. Shiryaev, Two problems of sequential analysis, Cybernetics, vol.X, issue.2, pp.79-86, 1967.
DOI : 10.1007/BF01078755

A. N. Shiryaev, Optimal Stopping Rules, 1978.
DOI : 10.1007/978-3-642-04898-2_433

A. N. Shiryaev, Quickest Detection Problems in the Technical Analysis of the Financial Data, Proc. Math. Finance Bachelier Congress, pp.487-521, 2000.
DOI : 10.1007/978-3-662-12429-1_22

A. N. Shiryaev, Z. Xu, and X. Zhou, Thou shalt buy and hold, Quantitative Finance, vol.8, issue.8, pp.765-776, 2008.
DOI : 10.1007/s002450010003

S. E. Shreve and H. M. Soner, Optimal Investment and Consumption with Transaction Costs, The Annals of Applied Probability, vol.4, issue.3, pp.609-692, 1994.
DOI : 10.1214/aoap/1177004966

R. Tevzadze, Solvability of backward stochastic differential equations with quadratic growth, Stochastic Processes and their Applications, vol.118, issue.3, pp.503-515, 2008.
DOI : 10.1016/j.spa.2007.05.009

M. A. Urusov, On a Property of the Moment at Which Brownian Motion Attains Its Maximum and Some Optimal Stopping Problems, Theory of Probability & Its Applications, vol.49, issue.1, pp.169-176, 2005.
DOI : 10.1137/S0040585X97980956

T. B. Veblen, The Theory of the Leisure Class: an Economic Study of Institutions, 1899.

T. Zariphopoulou, Consumption-Investment Models with Constraints, SIAM Journal on Control and Optimization, vol.32, issue.1, pp.59-85, 1994.
DOI : 10.1137/S0363012991218827

T. Zariphopoulou, A solution approach to valuation with unhedgeable risks, Finance and Stochastics, vol.5, issue.1, pp.61-82, 2001.
DOI : 10.1007/PL00000040

H. Zhang and Q. Zhang, Trading a mean-reverting asset: Buy low and sell high, Automatica, vol.44, issue.6, pp.1511-1518, 2008.
DOI : 10.1016/j.automatica.2007.11.003