V. V. Acharya and L. H. Pedersen, Asset pricing with liquidity risk, Journal of Financial Economics, vol.77, issue.2, pp.375-410, 2005.
DOI : 10.1016/j.jfineco.2004.06.007

T. Adrian and J. Rosenberg, Stock Returns and Volatility: Pricing the Short-Run and Long-Run Components of Market Risk, SSRN Electronic Journal, vol.63, issue.6, pp.2997-3030, 2008.
DOI : 10.2139/ssrn.918479

Y. Ait-sahalia and R. Kimmel, Maximum likelihood estimation of stochastic volatility models, Journal of Financial Economics, vol.83, issue.2, pp.413-452, 2007.
DOI : 10.3386/w10579

A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods and Applications, vol.11, issue.4, p.355, 2005.
DOI : 10.1515/156939605777438569

S. Alizadeh, M. W. Brandt, and F. X. Diebold, Range-Based Estimation of Stochastic Volatility Models, The Journal of Finance, vol.73, issue.3, pp.1047-1091, 2002.
DOI : 10.1111/1540-6261.00454

T. G. Andersen, Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility, The Journal of Finance, vol.51, issue.1, pp.169-204, 1996.
DOI : 10.1111/j.1540-6261.1996.tb05206.x

T. G. Andersen and T. Bollerslev, Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies, The Journal of Finance, vol.14, issue.1, pp.219-265, 1998.
DOI : 10.1111/0022-1082.85732

T. G. Andersen, T. Bollerslev, and F. X. Diebold, Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. The review of economics and statistics, pp.701-720, 2007.

B. D. Anderson and J. B. Moore, Optimal Filtering, IEEE Transactions on Systems, Man, and Cybernetics, vol.12, issue.2, 2012.
DOI : 10.1109/TSMC.1982.4308806

T. W. Anderson, The statistical analysis of time series, 2011.

E. Andreou and E. Ghysels, Detecting multiple breaks in financial market volatility dynamics, Journal of Applied Econometrics, vol.6, issue.5, pp.579-600, 2002.
DOI : 10.1002/jae.684
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.5274

T. Ané and H. Geman, Order Flow, Transaction Clock, and Normality of Asset Returns, The Journal of Finance, vol.45, issue.5, pp.2259-2284, 2000.
DOI : 10.1111/0022-1082.00286

A. Ang and G. Bekaert, Stock Return Predictability: Is it There?, Review of Financial Studies, vol.20, issue.3, p.651, 2007.
DOI : 10.1093/rfs/hhl021
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.194.6371

A. Ang and M. Piazzesi, A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables, Journal of Monetary Economics, vol.50, issue.4, pp.745-787, 2003.
DOI : 10.1016/S0304-3932(03)00032-1

D. Avramov, T. Chordia, and A. Goyal, Liquidity and Autocorrelations in Individual Stock Returns, The Journal of Finance, vol.102, issue.5, pp.2365-2394, 2006.
DOI : 10.1111/j.1540-6261.2006.01060.x

L. Bachelier, Th??orie de la sp??culation, Annales scientifiques de l'??cole normale sup??rieure, vol.17, 1900.
DOI : 10.24033/asens.476

P. Bajgrowicz, O. Scaillet, and A. Treccani, Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News, Management Science, vol.62, issue.8, 2015.
DOI : 10.1287/mnsc.2015.2234

M. Baker and J. Wurgler, The Equity Share In New Issues And Aggregate Stock Returns, SSRN Electronic Journal, vol.55, issue.5, pp.2219-2257, 2000.
DOI : 10.2139/ssrn.172548

N. Barberis, Investing for the Long Run when Returns Are Predictable, The Journal of Finance, vol.60, issue.1, pp.225-264, 2000.
DOI : 10.1111/0022-1082.00205
URL : http://badger.som.yale.edu/faculty/ncb25/alloc_jnl.pdf

N. Barberis, M. Huang, and T. Santos, Prospect theory and asset prices, Quarterly Journal of Economics, vol.116, issue.1, 2001.
DOI : 10.2139/ssrn.169790
URL : http://badger.som.yale.edu/faculty/ncb25/bhs_jnl.pdf

H. Barreto and F. Howland, Introductory econometrics: using Monte Carlo simulation with Microsoft excel, 2006.
DOI : 10.1017/CBO9780511809231

P. Barrieu and N. Karoui, Pricing, hedging, and designing derivatives with risk measures., indifference pricing: Theory and applications, 2009.
DOI : 10.1515/9781400833115.77

S. Basak, A General Equilibrium Model of Portfolio Insurance, Review of Financial Studies, vol.8, issue.4, pp.1059-1090, 1995.
DOI : 10.1093/rfs/8.4.1059

S. Basak and A. Shapiro, Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices, Review of Financial Studies, vol.14, issue.2, pp.371-405, 2001.
DOI : 10.1093/rfs/14.2.371
URL : http://rfs.oxfordjournals.org/cgi/content/short/14/2/371

S. Benartzi and R. H. Thaler, Myopic loss aversion and the equity premium puzzle, The Quarterly Journal of Economics, 1995.
DOI : 10.2307/2118511
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.353.2566

A. Berkaoui, M. Bossy, and A. Diop, Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence, ESAIM: Probability and Statistics 12, 2008.
DOI : 10.1051/ps:2007030
URL : https://hal.archives-ouvertes.fr/inria-00000176

A. B. Berkelaar, R. Kouwenberg, and T. Post, Optimal Portfolio Choice under Loss Aversion, Review of Economics and Statistics, vol.78, issue.4, pp.973-987, 2004.
DOI : 10.2307/1911158
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.3098

C. Bernard and M. Ghossoub, Static portfolio choice under Cumulative Prospect Theory, Mathematics and Financial Economics, vol.55, issue.1, pp.277-306, 2010.
DOI : 10.1007/s11579-009-0021-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.570.9196

H. Bessembinder and P. J. Seguin, Price Volatility, Trading Volume, and Market Depth: Evidence from Futures Markets, The Journal of Financial and Quantitative Analysis, vol.28, issue.1, pp.21-39, 1993.
DOI : 10.2307/2331149

J. Bia-lkowski, S. Darolles, and G. L. Fol, Improving VWAP strategies: A dynamic volume approach, Journal of Banking & Finance, vol.32, issue.9, pp.1709-1722, 2008.
DOI : 10.1016/j.jbankfin.2007.09.023

V. Binsbergen, H. Jules, and R. S. Koijen, Predictive Regressions: A Present-Value Approach, The Journal of Finance, vol.54, issue.4, pp.1439-1471, 2010.
DOI : 10.1111/j.1540-6261.2010.01575.x

F. Black and A. Perold, Theory of constant proportion portfolio insurance, Journal of Economic Dynamics and Control, vol.16, issue.3-4, pp.3-4, 1992.
DOI : 10.1016/0165-1889(92)90043-E

F. Black and R. Rouhani, Constant proportion portfolio insurance and the synthetic put option: a comparison, Institutional Investor focus on Investment Management, pp.695-708, 1989.

T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, vol.31, issue.3, pp.307-327, 1986.
DOI : 10.1016/0304-4076(86)90063-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.7380

T. Bollerslev, L. Xu, and H. Zhou, Stock return and cash flow predictability: The role of volatility risk, Journal of Econometrics, vol.187, issue.2, pp.458-471, 2015.
DOI : 10.1016/j.jeconom.2015.02.031

M. Bossy and A. Diop, An efficient discretisation scheme for one dimensional sdes with a diffusion coefficient function of the form| x|â, a in, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00000177

B. Bouchard, R. Elie, and C. Imbert, Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3501-3531, 2010.
DOI : 10.1137/090757629
URL : https://hal.archives-ouvertes.fr/hal-00373306

B. Bouchard, R. Elie, and N. Touzi, Stochastic Target Problems with Controlled Loss, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3123-3150, 2009.
DOI : 10.1137/08073593X
URL : https://hal.archives-ouvertes.fr/hal-00323383

P. Boyle and W. Tian, PORTFOLIO MANAGEMENT WITH CONSTRAINTS, Mathematical Finance, vol.116, issue.4, pp.319-343, 2007.
DOI : 10.1016/S0022-0531(03)00062-0
URL : http://belkcollegeofbusiness.uncc.edu/wtian1/mafi_306.pdf

M. W. Brandt and Q. Kang, On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach, Journal of Financial Economics, vol.72, issue.2, pp.217-257, 2004.
DOI : 10.1016/j.jfineco.2002.06.001

M. J. Brennan and E. S. Schwartz, Portfolio Insurance and Financial Market Equilibrium, The Journal of Business, vol.62, issue.4, pp.455-472, 1989.
DOI : 10.1086/296472

M. J. Brennan and R. Solanki, Optimal Portfolio Insurance, The Journal of Financial and Quantitative Analysis, vol.16, issue.3, pp.279-300, 1981.
DOI : 10.2307/2330239

D. Brigo and A. Alfonsi, Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model, Finance and Stochastics, vol.9, issue.1, pp.29-42, 2005.
DOI : 10.1007/s00780-004-0131-x

J. Campbell, S. Grossman, and J. Wang, Trading Volume and Serial Correlation in Stock Returns, The Quarterly Journal of Economics, vol.108, issue.4, pp.905-939, 1993.
DOI : 10.2307/2118454

J. Campbell and R. Shiller, The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors, Review of Financial Studies, vol.1, issue.3, pp.195-228, 1988.
DOI : 10.1093/rfs/1.3.195

J. Y. Campbell, Stock returns and the term structure, Journal of Financial Economics, vol.18, issue.2, pp.373-399, 1987.
DOI : 10.1016/0304-405X(87)90045-6

J. Y. Campbell, A variance decomposition for stock returns, National Bureau of Economic Research, 1991.

J. Y. Campbell and J. Ammer, What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns, The Journal of Finance, vol.1, issue.1, pp.3-37, 1993.
DOI : 10.1111/j.1540-6261.1993.tb04700.x

J. Y. Campbell and S. B. Thompson, Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?, Review of Financial Studies, vol.21, issue.4, pp.1509-1531, 2008.
DOI : 10.1093/rfs/hhm055

L. Carassus, M. Rásonyi, and A. M. Rodrigues, Non-concave utility maximisation on the positive real axis in discrete time, Mathematics and Financial Economics, vol.5, issue.4, pp.325-349, 2015.
DOI : 10.1007/s11579-015-0146-4

C. K. Carter and R. Kohn, On Gibbs sampling for state space models, Biometrika, vol.81, issue.3, pp.541-553, 1994.
DOI : 10.1093/biomet/81.3.541

C. M. Carvalho, H. F. Lopes, and R. E. Mcculloch, On the Long Run Volatility of Stocks, SSRN Electronic Journal, 2015.
DOI : 10.2139/ssrn.2808191

M. Chernov, A. R. Gallant, E. Ghysels, and G. Tauchen, Alternative models for stock price dynamics, Journal of Econometrics, vol.116, issue.1-2, pp.225-257, 2003.
DOI : 10.1016/S0304-4076(03)00108-8
URL : https://www.elsevier.com/understand-publishing

V. Cherny and J. Ob-lój, Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model, Finance and Stochastics, vol.19, issue.4, pp.771-800, 2013.
DOI : 10.1007/s00780-013-0209-4

P. K. Clark, A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, Econometrica, vol.41, issue.1, pp.135-155, 1973.
DOI : 10.2307/1913889
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.6859

J. Cochrane, The Dog That Did Not Bark: A Defense of Return Predictability, Review of Financial Studies, vol.21, issue.4, p.1533, 2008.
DOI : 10.1093/rfs/hhm046

J. H. Cochrane, Time series for macroeconomics and finance, 2005.

R. Colacito, R. F. Engle, and E. Ghysels, A component model for dynamic correlations, Journal of Econometrics, vol.164, issue.1, pp.45-59, 2011.
DOI : 10.1016/j.jeconom.2011.02.013

J. Conrad and G. Kaul, Time-Variation in Expected Returns, The Journal of Business, vol.61, issue.4, pp.409-425, 1988.
DOI : 10.1086/296441

R. Cont and P. Tankov, CONSTANT PROPORTION PORTFOLIO INSURANCE IN THE PRESENCE OF JUMPS IN ASSET PRICES, Mathematical Finance, vol.23, issue.2, pp.379-401, 2009.
DOI : 10.1111/j.1467-9965.2009.00377.x
URL : https://hal.archives-ouvertes.fr/hal-00415514

M. Cooper, Filter Rules Based on Price and Volume in Individual Security Overreaction, Review of Financial Studies, vol.12, issue.4, pp.901-935, 1999.
DOI : 10.1093/rfs/12.4.901

J. Cox and H. Leland, Notes on intertemporal investment policies, 1982.

J. C. Cox, J. E. Ingersoll-jr, and S. A. Ross, A theory of the term structure of interest rates, Econometrica: Journal of the Econometric Society, pp.385-407, 1985.

J. Cujean and M. Hasler, Why does return predictability concentrate in bad times?, 2014.

J. Cvitanic and I. Karatzas, On Portfolio Optimization under ???Drawdown??? Constraints, IMA Volumes in Mathematics and its Applications, vol.65, pp.35-35, 1995.
DOI : 10.1007/978-1-4757-2435-6_3

Z. Da, Q. Liu, and E. Schaumburg, A Closer Look at the Short-Term Return Reversal, Management Science, vol.60, issue.3, pp.658-674, 2013.
DOI : 10.1287/mnsc.2013.1766

T. Dangl and M. Halling, Predictive regressions with time-varying coefficients, Journal of Financial Economics, 2012.
DOI : 10.1016/j.jfineco.2012.04.003
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7559

S. Darolles, G. L. Fol, and G. Mero, Measuring the liquidity part of volume, Journal of Banking & Finance, vol.50, pp.92-105, 2015.
DOI : 10.1016/j.jbankfin.2014.09.007

D. Brouwer, P. , and F. Van, The fallacy of large numbers revisited: The construction of a utility function that leads to the acceptance of two games, while one is rejected, Journal of Asset Management, vol.1, issue.3, pp.257-266, 2001.
DOI : 10.1057/palgrave.jam.2240020

H. Dichtl and W. Drobetz, Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products, Journal of Banking & Finance, vol.35, issue.7, pp.1683-1697, 2011.
DOI : 10.1016/j.jbankfin.2010.11.012

M. Dierkes, C. Erner, and S. Zeisberger, Investment horizon and the attractiveness of investment strategies: A behavioral approach, Journal of Banking & Finance, vol.34, issue.5, pp.1032-1046, 2010.
DOI : 10.1016/j.jbankfin.2009.11.003

Z. Ding and C. W. Granger, Modeling volatility persistence of speculative returns: A new approach, Journal of Econometrics, vol.73, issue.1, pp.185-215, 1996.
DOI : 10.1016/0304-4076(95)01737-2

G. R. Duffee, Are variations in term premia related to the macroeconomy. Unpublished working paper, 2007.

D. Duffie, Dynamic asset pricing theory, 2010.

S. Ebert, B. Koos, and J. C. Schneider, On the Optimal Type and Level of Guarantees for Prospect Theory Investors, Paris December 2012 Finance Meeting EUROFIDAI-AFFI Paper, 2012.
DOI : 10.2139/ssrn.2081665

E. Karoui, N. , M. Jeanblanc, and V. Lacoste, Optimal portfolio management with American capital guarantee, Journal of Economic Dynamics and Control, vol.29, issue.3, pp.449-468, 2005.
DOI : 10.1016/j.jedc.2003.11.005

E. Karoui, N. , and A. Meziou, CONSTRAINED OPTIMIZATION WITH RESPECT TO STOCHASTIC DOMINANCE: APPLICATION TO PORTFOLIO INSURANCE, Mathematical Finance, vol.16, issue.1, pp.103-117, 2006.
DOI : 10.1016/0022-0531(70)90038-4

R. Elie, Contrôle stochastique et méthodes numériques en finance mathématique, 2006.

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

R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, pp.987-1008, 1982.
DOI : 10.2307/1912773

R. F. Engle, Discussion, Review of Financial Studies, vol.3, issue.1, pp.103-109, 1990.
DOI : 10.1093/rfs/3.1.103

R. F. Engle, E. Ghysels, and B. Sohn, Stock Market Volatility and Macroeconomic Fundamentals, Review of Economics and Statistics, vol.62, issue.3, pp.776-797, 2013.
DOI : 10.1086/296513

R. F. Engle and C. W. Granger, Co-integration and error correction: representation, estimation, and testing, Econometrica: journal of the Econometric Society, pp.251-276, 1987.
DOI : 10.1017/ccol052179207x.009

R. F. Engle and G. Lee, A permanent and transitory component model of stock return volatility. Cointegration , Causality, and Forecasting: A Festschrift in Honour of Clive WJ Granger, pp.475-497, 1999.

R. F. Engle and J. G. Rangel, The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes, Review of Financial Studies, vol.21, issue.3, pp.1187-1222, 2008.
DOI : 10.1093/rfs/hhn004

R. F. Engle and M. E. Sokalska, Forecasting intraday volatility in the US equity market. Multiplicative component GARCH, Journal of Financial Econometrics, vol.10, issue.1, pp.54-83, 2012.
DOI : 10.1093/jjfinec/nbr005

T. W. Epps and M. L. Epps, The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis, Econometrica, vol.44, issue.2, pp.305-326, 1976.
DOI : 10.2307/1912726

T. Estep and M. Kritzman, TIPP, The Journal of Portfolio Management, vol.14, issue.4, pp.38-42, 1988.
DOI : 10.3905/jpm.1988.409172

E. F. Fama and K. R. French, Dividend yields and expected stock returns, Journal of Financial Economics, vol.22, issue.1, pp.3-25, 1988.
DOI : 10.1016/0304-405X(88)90020-7

E. F. Fama and K. R. French, Business conditions and expected returns on stocks and bonds, Journal of Financial Economics, vol.25, issue.1, pp.23-49, 1989.
DOI : 10.1016/0304-405X(89)90095-0

W. Feller, Two singular diffusion problems, Annals of mathematics, pp.173-182, 1951.
DOI : 10.2307/1969318

W. E. Ferson and C. R. Harvey, The Variation of Economic Risk Premiums, Journal of Political Economy, vol.99, issue.2, pp.385-415, 1991.
DOI : 10.1086/261755

J. Fleming, C. Kirby, and B. Ostdiek, ARCH Effects and Trading Volume, SSRN Electronic Journal, 2005.
DOI : 10.2139/ssrn.803838

J. Fleming, C. Kirby, and B. Ostdiek, Stochastic Volatility, Trading Volume, and the Daily Flow of Information*, The Journal of Business, vol.79, issue.3, pp.1551-1590, 2006.
DOI : 10.1086/500685

P. Forsyth and G. Labahn, Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance, The Journal of Computational Finance, vol.11, issue.2, pp.1-44, 2008.
DOI : 10.21314/JCF.2007.163

F. D. Foster and S. Viswanathan, Can speculative trading explain the volume?volatility relation, Journal of Business & Economic Statistics, vol.13, issue.4, pp.379-396, 1995.
DOI : 10.2307/1392384

S. Frühwirth-schnatter, DATA AUGMENTATION AND DYNAMIC LINEAR MODELS, Journal of Time Series Analysis, vol.38, issue.2, pp.183-202, 1994.
DOI : 10.2307/2289457

A. R. Gallant, C. Hsu, and G. Tauchen, Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance, Review of Economics and Statistics, vol.80, issue.4, pp.617-631, 1999.
DOI : 10.1016/0304-4076(95)01755-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.162

A. R. Gallant, P. E. Rossi, and G. Tauchen, Stock Prices and Volume, Review of Financial Studies, vol.5, issue.2, pp.199-242, 1992.
DOI : 10.1093/rfs/5.2.199

E. Ghysels, A. C. Harvey, and E. Renault, 5 stochastic volatility. Handbook of statistics 14, pp.119-191, 1996.

L. R. Glosten, R. Jagannathan, and D. E. Runkle, On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, The Journal of Finance, vol.25, issue.5, pp.1779-1801, 1993.
DOI : 10.1111/j.1540-6261.1993.tb05128.x

T. Gneiting, Making and Evaluating Point Forecasts, Journal of the American Statistical Association, vol.106, issue.494, pp.746-762, 2011.
DOI : 10.1198/jasa.2011.r10138
URL : http://arxiv.org/abs/0912.0902

W. N. Goetzmann and P. Jorion, Testing the Predictive Power of Dividend Yields, The Journal of Finance, vol.48, issue.2, pp.663-679, 1993.
DOI : 10.1111/j.1540-6261.1993.tb04732.x

F. J. Gomes, Portfolio Choice and Trading Volume with Loss???Averse Investors, The Journal of Business, vol.78, issue.2, pp.675-706, 2005.
DOI : 10.1086/427643

C. Gouriéroux and J. Jasiak, Autoregressive gamma processes, Journal of Forecasting, vol.10, issue.2, pp.129-152, 2006.
DOI : 10.1002/for.978

A. Goyal and I. Welch, Predicting the Equity Premium with Dividend Ratios, Management Science, vol.49, issue.5, pp.639-654, 2003.
DOI : 10.1287/mnsc.49.5.639.15149

A. Goyal and I. Welch, A Comprehensive Look at The Empirical Performance of Equity Premium Prediction, Review of Financial Studies, vol.21, issue.4, p.1455, 2008.

B. Graham, D. L. Dodd, and S. Cottle, Security analysis, 1934.

M. Grinblatt and B. Han, Prospect theory, mental accounting, and momentum, Journal of Financial Economics, vol.78, issue.2, pp.311-339, 2005.
DOI : 10.1016/j.jfineco.2004.10.006

S. J. Grossman and J. Vila, Portfolio Insurance in Complete Markets: A Note, The Journal of Business, vol.62, issue.4, pp.473-476, 1989.
DOI : 10.1086/296473

S. J. Grossman and Z. Zhou, OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS, Mathematical Finance, vol.13, issue.2, pp.241-276, 1993.
DOI : 10.1016/0022-0531(71)90038-X

S. J. Grossman and Z. Zhou, Equilibrium Analysis of Portfolio Insurance, The Journal of Finance, vol.49, issue.4, pp.1379-1403, 1996.
DOI : 10.1111/j.1540-6261.1996.tb04073.x

L. Grüne and W. Semmler, Asset pricing with loss aversion, Journal of Economic Dynamics and Control, vol.32, issue.10, pp.3253-3274, 2008.
DOI : 10.1016/j.jedc.2008.01.002

M. S. Haigh and J. A. List, Do Professional Traders Exhibit Myopic Loss Aversion? An Experimental Analysis, The Journal of Finance, vol.112, issue.1, pp.523-534, 2005.
DOI : 10.1111/j.1540-6261.2005.00737.x

B. Hamidi, B. Maillet, and J. Prigent, A dynamic autoregressive expectile for time-invariant portfolio protection strategies, Journal of Economic Dynamics and Control, vol.46, pp.1-29, 2014.
DOI : 10.1016/j.jedc.2014.05.005
URL : https://hal.archives-ouvertes.fr/halshs-01015390

J. D. Hamilton and G. Lin, Stock market volatility and the business cycle, Journal of Applied Econometrics, vol.25, issue.5, pp.573-593, 1996.
DOI : 10.1002/(SICI)1099-1255(199609)11:5<573::AID-JAE413>3.0.CO;2-T

B. E. Hansen, Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis, Econometrica, vol.64, issue.2, pp.413-430, 1996.
DOI : 10.2307/2171789
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.2004

M. Harris and A. Raviv, Differences of Opinion Make a Horse Race, Review of Financial Studies, vol.6, issue.3, pp.473-506, 1993.
DOI : 10.1093/rfs/5.3.473

X. D. He and X. Y. Zhou, Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment, Management Science, vol.57, issue.2, pp.315-331, 2011.
DOI : 10.1287/mnsc.1100.1269

J. J. Heckman, Statistical models for discrete panel data, 1979.

S. J. Henkel, J. S. Martin, and F. Nardari, Time-varying short-horizon predictability???, Journal of Financial Economics, vol.99, issue.3, pp.560-580, 2011.
DOI : 10.1016/j.jfineco.2010.09.008

C. Hiemstra and J. D. Jones, Testing for linear and nonlinear granger causality in the stock price-volume relation, The Journal of Finance, vol.49, issue.5, pp.1639-1664, 1994.

D. A. Hsieh, Modeling heteroscedasticity in daily foreign-exchange rates, Journal of Business & Economic Statistics, vol.7, issue.3, pp.307-317, 1989.
DOI : 10.1080/07350015.1989.10509740

H. Jin and X. Y. Zhou, BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME, Mathematical Finance, vol.42, issue.3, pp.385-426, 2008.
DOI : 10.1111/j.1467-9965.2008.00339.x
URL : http://arxiv.org/abs/0709.2830

M. Johannes, A. Korteweg, and N. Polson, Sequential Learning, Predictability, and Optimal Portfolio Returns, The Journal of Finance, vol.56, issue.2, pp.611-644, 2014.
DOI : 10.1111/0022-1082.00323

D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica: Journal of the Econometric Society, pp.263-291, 1979.

J. M. Karpoff, The Relation Between Price Changes and Trading Volume: A Survey, The Journal of Financial and Quantitative Analysis, vol.22, issue.1, pp.109-126, 1987.
DOI : 10.2307/2330874

D. B. Keim and R. F. Stambaugh, Predicting returns in the stock and bond markets, Journal of Financial Economics, vol.17, issue.2, pp.357-390, 1986.
DOI : 10.1016/0304-405X(86)90070-X

B. Kelly and S. Pruitt, Market Expectations in the Cross-Section of Present Values, The Journal of Finance, vol.48, issue.5, pp.1721-1756, 2013.
DOI : 10.1111/jofi.12060

A. Khuman, N. Constantinou, and S. Phelps, Constant Proportion Portfolio Insurance Strategies under Cumulative Prospect Theory with Reference Point Adaptation, SSRN Electronic Journal, 2012.
DOI : 10.2139/ssrn.2109551
URL : http://repository.essex.ac.uk/8127/1/WP%202012-7%20Constantinou.pdf

C. Kim and C. R. Nelson, State-space models with regime switching: classical and gibbs-sampling approaches with applications, 1999.

M. J. Klass and K. Nowicki, The Grossman and Zhou investment strategy is not always optimal, Statistics & Probability Letters, vol.74, issue.3, pp.245-252, 2005.
DOI : 10.1016/j.spl.2005.04.060

K. Kva??áková, Is imperfection better? evidence from predicting stock and bond returns. Unpublished working paper, 2013.

D. Kwiatkowski, P. C. Phillips, P. Schmidt, and Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of Econometrics, vol.54, issue.1-3, pp.159-178, 1992.
DOI : 10.1016/0304-4076(92)90104-Y

C. G. Lamoureux and W. D. Lastrapes, Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects, The Journal of Finance, vol.12, issue.1, pp.221-229, 1990.
DOI : 10.1111/j.1540-6261.1990.tb05088.x

C. G. Lamoureux and W. D. Lastrapes, Persistence in variance, structural change, and the garch model, Journal of Business & Economic Statistics, vol.8, issue.2, pp.225-234, 1990.

C. G. Lamoureux and W. D. Lastrapes, Endogenous Trading Volume and Momentum in Stock-Return Volatility, Journal of Business & Economic Statistics, vol.51, issue.2, pp.253-260, 1994.
DOI : 10.1080/07350015.1994.10510012

C. G. Lamoureux and G. Zhou, Temporary Components of Stock Returns: What Do the Data Tell Us?, Review of Financial Studies, vol.9, issue.4, pp.1033-1059, 1996.
DOI : 10.1093/rfs/9.4.1033

P. K. Lattimore, J. R. Baker, and A. D. Witte, The influence of probability on risky choice: A parametric examination, Journal of Economic Behavior & Organization, vol.17, issue.3, pp.377-400, 1992.

H. Leland and M. Rubinstein, Portfolio insurance: A guide to dynamic hedging. The evolution of portfolio insurance, 1976.

H. E. Leland, Who Should Buy Portfolio Insurance?, The Journal of Finance, vol.36, issue.2, pp.581-594, 1980.
DOI : 10.1111/j.1540-6261.1980.tb02190.x

D. Lépingle, Euler scheme for reflected stochastic differential equations, Mathematics and Computers in Simulation, vol.38, issue.1-3, pp.119-126, 1995.
DOI : 10.1016/0378-4754(93)E0074-F

M. Lettau and S. Ludvigson, Consumption, aggregate wealth, and expected stock returns, Journal of Finance, pp.815-849, 2001.
DOI : 10.2139/ssrn.169791
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.196.6466

M. Lettau and S. Van-nieuwerburgh, Reconciling the Return Predictability Evidence, Review of Financial Studies, vol.21, issue.4, p.1607, 2008.
DOI : 10.1093/rfs/hhm074

R. Liesenfeld, Dynamic BivarSate Mixture Models: Modeling the Behavior of Prices and Trading Volume, Journal of Business & Economic Statistics, vol.51, issue.1, pp.101-109, 1998.
DOI : 10.1080/07350015.1998.10524739

G. Llorente, R. Michaely, G. Saar, and J. Wang, Dynamic Volume-Return Relation of Individual Stocks, Review of Financial Studies, vol.15, issue.4, pp.1005-1047, 2002.
DOI : 10.1093/rfs/15.4.1005

A. W. Lo and J. Wang, Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory, Review of Financial Studies, vol.13, issue.2, pp.257-300, 2000.
DOI : 10.1093/rfs/13.2.257

J. M. Maheu and T. H. Mccurdy, News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns, The Journal of Finance, vol.11, issue.2, pp.755-793, 2004.
DOI : 10.1111/j.1540-6261.2004.00648.x
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.391.8239

D. Mantilla-garcia and V. Vaidyanathan, Predicting Stock Returns in the presence of Uncertain Structural Breaks and Sample Noise. Working Paper, Edhec Business School, 2011.

M. Mccracken, Asymptotics for out of sample tests of Granger causality, Journal of Econometrics, vol.140, issue.2, pp.719-752, 2007.
DOI : 10.1016/j.jeconom.2006.07.020

R. Merton, Influence of Mathematical Models in Finance on Practice: Past, Present and Future [and Discussion], Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.347, issue.1684, pp.1-14, 1995.
DOI : 10.1098/rsta.1994.0055

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, On estimating the expected return on the market: An exploratory investigation, Journal of Financial Economics, vol.8, issue.4, pp.323-361, 1980.
DOI : 10.3386/w0444

R. C. Merton, Chapter 13 On the microeconomic theory of investment under uncertainty, Handbook of Mathematical Economics, vol.2, pp.601-669, 1993.
DOI : 10.1016/S1573-4382(82)02008-6

A. Meucci, Differences and commonalities between the two areas of quantitative finance. The Quant Classroom by Attilio Meucci -GARP Risk Professional, pp.47-50, 2011.

K. M. Murphy and R. H. , Estimation and Inference in Two-Step Econometric Models, Journal of Business & Economic Statistics, vol.20, issue.1, pp.88-97, 2002.
DOI : 10.1198/073500102753410417

D. B. Nelson, ARCH models as diffusion approximations, Journal of Econometrics, vol.45, issue.1-2, pp.7-38, 1990.
DOI : 10.1016/0304-4076(90)90092-8

D. B. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, vol.59, issue.2, pp.347-370, 1991.
DOI : 10.2307/2938260

G. Pages and F. Panloup, Approximation of the distribution of a stationary Markov process with application to option pricing, Bernoulli, vol.15, issue.1, p.146, 2009.
DOI : 10.3150/08-BEJ142
URL : https://hal.archives-ouvertes.fr/hal-00358792

L. Pastor and R. F. Stambaugh, Liquidity risk and expected stock returns, Journal of Political Economy, vol.111, issue.3, 2003.

L. Pástor and R. F. Stambaugh, Predictive Systems: Living with Imperfect Predictors, The Journal of Finance, vol.54, issue.1, pp.1583-1628, 2009.
DOI : 10.1111/j.1540-6261.2009.01474.x

L. Pástor and R. F. Stambaugh, Are Stocks Really Less Volatile in the Long Run?, The Journal of Finance, vol.2, issue.2, pp.431-478, 2012.
DOI : 10.1111/j.1540-6261.2012.01722.x

M. H. Pesaran and A. Timmermann, Predictability of Stock Returns: Robustness and Economic Significance, The Journal of Finance, vol.108, issue.4, pp.1201-1228, 1995.
DOI : 10.1111/j.1540-6261.1995.tb04055.x

D. Pettenuzzo and F. Ravazzolo, Optimal Portfolio Choice Under Decision-Based Model Combinations, Journal of Applied Econometrics, vol.21, issue.1, 2014.
DOI : 10.1002/jae.2502
URL : https://brage.bibsys.no/xmlui/bitstream/11250/2365020/1/Working_CAMP_9-2015.pdf

D. Pettenuzzo, A. Timmermann, and R. Valkanov, Forecasting stock returns under economic constraints, Journal of Financial Economics, 2014.
DOI : 10.2139/ssrn.2186574
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.404.5022

I. Piatti and F. Trojani, Dividend Growth Predictability and the Price-Dividend Ratio, SSRN Electronic Journal, 2014.
DOI : 10.2139/ssrn.2077381
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.2033

I. Piatti and F. Trojani, Predictable Risks and Predictive Regression in Present-Value Models, SSRN Electronic Journal, 2015.
DOI : 10.2139/ssrn.1786897

D. Rapach, J. Strauss, and G. Zhou, Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy, Review of Financial Studies, vol.23, issue.2, p.821, 2010.
DOI : 10.1093/rfs/hhp063

M. Richardson and T. Smith, A Direct Test of the Mixture of Distributions Hypothesis: Measuring the Daily Flow of Information, The Journal of Financial and Quantitative Analysis, vol.29, issue.1, pp.101-116, 1994.
DOI : 10.2307/2331193

S. A. Ross, Adding Risks: Samuelson's Fallacy of Large Numbers Revisited, The Journal of Financial and Quantitative Analysis, vol.34, issue.3, pp.323-339, 1999.
DOI : 10.2307/2676262

P. J. Rousseeuw and K. V. Driessen, A Fast Algorithm for the Minimum Covariance Determinant Estimator, Technometrics, vol.35, issue.3, pp.212-223, 1999.
DOI : 10.1080/01621459.1994.10476821

O. Rytchkov, Filtering Out Expected Dividends and Expected Returns, Quarterly Journal of Finance, vol.02, issue.03, 2012.
DOI : 10.1142/S2010139212500127
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.3249

P. Samuelson, Risk and uncertainty: A fallacy of large numbers, Scientia, vol.98, issue.4-5, pp.108-113, 1963.

G. W. Schwert, Why Does Stock Market Volatility Change Over Time?, The Journal of Finance, vol.28, issue.5, pp.1115-1153, 1989.
DOI : 10.1111/j.1540-6261.1989.tb02647.x

C. T. Shalen, Volume, Volatility, and the Dispersion of Beliefs, Review of Financial Studies, vol.6, issue.2, pp.405-434, 1993.
DOI : 10.1093/rfs/6.2.405

R. F. Stambaugh, Bias in Regressions with Lagged Stochastic Regressors, 1986.

R. F. Stambaugh, Predictive regressions, Journal of Financial Economics, vol.54, issue.3, pp.375-421, 1999.
DOI : 10.1016/S0304-405X(99)00041-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.199.3478

G. E. Tauchen and M. Pitts, The Price Variability-Volume Relationship on Speculative Markets, Econometrica, vol.51, issue.2, pp.485-505, 1983.
DOI : 10.2307/1912002

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, vol.55, issue.1, pp.297-323, 1992.
DOI : 10.1007/BF00122574

J. H. Van-binsbergen and R. S. Koijen, Likelihood-Based Estimation of Exactly-Solved Present-Value Models, SSRN Electronic Journal, 2011.
DOI : 10.2139/ssrn.1439849

D. Vrecko and N. Branger, Why is portfolio insurance attractive to investors? Available at, 2009.
DOI : 10.2139/ssrn.1519344

J. Wang, A Model of Competitive Stock Trading Volume, Journal of Political Economy, vol.102, issue.1, pp.127-68, 1994.
DOI : 10.1086/261924

T. Watanabe, Bayesian Analysis of Dynamic Bivariate Mixture Models: Can They Explain the Behavior of Returns and Trading Volume?, Journal of Business & Economic Statistics, vol.21, issue.2, pp.199-210, 2000.
DOI : 10.1080/07350015.2000.10524862

M. Yang, Normal log-normal mixture, leptokurtosis and skewness, Applied Economics Letters, vol.15, issue.9, pp.737-742, 2008.
DOI : 10.1080/13504850600749073

C. C. Ying, Stock Market Prices and Volumes of Sales, Econometrica, vol.34, issue.3, pp.676-685, 1966.
DOI : 10.2307/1909776