A. Ahmadi-javid, Entropic Value-at-Risk: A New Coherent Risk Measure, Journal of Optimization Theory and Applications, vol.17, issue.3, pp.1105-1123, 2012.
DOI : 10.1007/s10957-011-9968-2

P. Artzner, F. Delbaen, J. Eber, D. Heath, and H. Ku, Coherent multiperiod risk adjusted values and Bellman???s principle, Annals of Operations Research, vol.10, issue.1, pp.5-22, 2007.
DOI : 10.1007/s10479-006-0132-6

P. Auer, N. Cesa-bianchi, and P. Fischer, Finite-time analysis of the multiarmed bandit problem, Machine Learning, vol.47, issue.2/3, pp.235-256, 2002.
DOI : 10.1023/A:1013689704352

P. Auer, Y. Nicoì-o-cesa-bianchi, R. E. Freund, and . Schapire, The Nonstochastic Multiarmed Bandit Problem, SIAM Journal on Computing, vol.32, issue.1, pp.48-77, 2003.
DOI : 10.1137/S0097539701398375

J. M. Borwein and A. S. Lewis, Duality Relationships for Entropy-Like Minimization Problems, SIAM Journal on Control and Optimization, vol.29, issue.2, pp.325-338, 1991.
DOI : 10.1137/0329017

A. N. Burnetas and M. N. Katehakis, Optimal Adaptive Policies for Sequential Allocation Problems, Advances in Applied Mathematics, vol.17, issue.2, pp.122-142, 1996.
DOI : 10.1006/aama.1996.0007

O. Cappé, A. Garivier, O. Maillard, R. Munos, and G. Stoltz, Kullback-leibler upper confidence bounds for optimal sequential allocation. The Annals of Statistics, 2013.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 1991.

B. Defourny, D. Ernst, and L. Wehenkel, Risk-aware decision making and dynamic programming, NIPS Workshop on Model Uncertainty and Risk in RL, 2008.

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 1998.
DOI : 10.1007/978-1-4612-5320-4

E. V. Denardo and U. G. Rothblum, Optimal stopping, exponential utility, and linear programming, Mathematical Programming, pp.228-244, 1979.
DOI : 10.1007/BF01582110

E. Even-dar, M. Kearns, and J. Wortman, Risk-Sensitive Online Learning, Proceedings of the 17th international conference on Algorithmic Learning Theory, 2006.
DOI : 10.1007/11894841_18

A. Garivier and O. Cappé, The KL-UCB algorithm for bounded stochastic bandits and beyond, Proceedings of the 24th Annual Conference on Learning Theory, 2011.

H. Harari-kermadec, Vraisemblance empirique généralisée et estimation semiparamétrique, 2006.

J. Honda and A. Takemura, An asymptotically optimal bandit algorithm for bounded support models, Proceedings of the 23rd Annual Conference on Learning Theory, 2010.

J. Honda and A. Takemura, An asymptotically optimal policy for finite support models in the multiarmed bandit problem, Machine Learning, vol.28, issue.3, pp.361-391, 2011.
DOI : 10.1007/s10994-011-5257-4

J. Honda and A. Takemura, Finite-time regret bound of a bandit algorithm for the semi-bounded support model, 2012.

A. Ronald, J. E. Howard, and . Matheson, Risk-sensitive markov decision processes, Management Science, vol.18, pp.356-369, 1972.

E. Kaufmann, N. Korda, and R. Munos, Thompson Sampling: An Asymptotically Optimal Finite-Time Analysis, Proceedings of the Algorithmic Learning Theory conference, pp.199-213, 2012.
DOI : 10.1007/978-3-642-34106-9_18
URL : https://hal.archives-ouvertes.fr/hal-00830033

T. L. Lai and H. Robbins, Asymptotically efficient adaptive allocation rules, Advances in Applied Mathematics, vol.6, issue.1, pp.4-22, 1985.
DOI : 10.1016/0196-8858(85)90002-8

Y. Liu and S. Koenig, An exact algorithm for solving mdps under risksensitive planning objectives with one-switch utility functions, pp.453-460, 2008.

O. Maillard, R. Munos, and G. Stoltz, A finite-time analysis of multi-armed bandits problems with Kullback-Leibler divergences, Proceedings of the 23rd Annual Conference on Learning Theory, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00574987

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

J. Neumann and O. Morgenstern, Theory of games and economic behavior, 1947.

D. Stephen and . Patek, On terminating markov decision processes with a risk-averse objective function, Automatica, vol.37, issue.9, pp.1379-1386, 2001.

H. Robbins, Some aspects of the sequential design of experiments, Bulletin of the American Mathematical Society, vol.58, issue.5, pp.527-535, 1952.
DOI : 10.1090/S0002-9904-1952-09620-8

R. Tyrrell-rockafellar, Coherent Approaches to Risk in Optimization Under Uncertainty, Tutorials in operation Research, pp.38-61, 2007.
DOI : 10.1287/educ.1073.0032

A. Salomon and J. Audibert, Robustness of stochastic bandit policies, Theoretical Computer Science, vol.519, 2012.
DOI : 10.1016/j.tcs.2013.09.019

A. Sani, A. Lazaric, and R. Munos, Risk-aversion in multi-armed bandits, Proceedings of Advancezs in neural information processing system, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00772609

W. R. Thompson, On the Likelihood that One Unknown Probability Exceeds Another in View of the Evidence of Two Samples, Biometrika, vol.25, issue.3/4, pp.285-294, 1933.
DOI : 10.2307/2332286

W. R. Thompson, On the Theory of Apportionment, American Journal of Mathematics, vol.57, issue.2, pp.450-456, 1935.
DOI : 10.2307/2371219

K. Manfred, D. Warmuth, and . Kuzmin, Online variance minimization, Proceedings of the 19th Annual Conference on Learning Theory, pp.514-528, 2006.