R. Adams and J. Fournier, Sobolev spaces, II edition, 2009.

P. Artzner, F. Delbaen, J. Eber, and D. Heath, Coherent Measures of Risk, Mathematical Finance, vol.9, issue.3, pp.203-228, 1999.
DOI : 10.1111/1467-9965.00068

R. Ash and C. Doléans-dade, Probability and measure theory, 2000.

G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stochastics An International Journal of Probability and Stochastic Processes, vol.60, issue.1, pp.57-83, 1997.
DOI : 10.1080/17442509708834099

G. Barles, E. Chasseigne, and C. Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana University Mathematics Journal, vol.57, issue.1, pp.213-146, 2008.
DOI : 10.1512/iumj.2008.57.3315

URL : https://hal.archives-ouvertes.fr/hal-00150151

G. Barles and C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions' theory revisited, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.25, issue.3, pp.567-585, 2008.
DOI : 10.1016/j.anihpc.2007.02.007

URL : https://hal.archives-ouvertes.fr/hal-00130169

P. Barrieu and N. Karoui, Optimal derivatives design under dynamic risk measures, p.13, 2004.
DOI : 10.1090/conm/351/06389

P. Barrieu and N. Karoui, Pricing, hedging and optimally designing derivatives via minimization of risk measures. Indifference Pricing, pp.77-141, 2008.

S. Basak and A. Shapiro, Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices, Review of Financial Studies, vol.14, issue.2, p.371, 2001.
DOI : 10.1093/rfs/14.2.371

A. Bensoussan and J. Lions, Impulse control and quasi-variational inequalities, 1984.

S. Biagini and M. Frittelli, On the extension of the namioka-klee theorem and on the fatou property for risk measures. Optimality and Risk-Modern Trends in Mathematical Finance, pp.1-28, 2009.

J. Bion-nadal, Dynamic risk measures: Time consistency and risk measures from BMO martingales, Finance and Stochastics, vol.9, issue.2, pp.219-244, 2008.
DOI : 10.1007/s00780-007-0057-1

J. Bion-nadal, Time consistent dynamic risk processes, Stochastic Processes and their Applications, pp.633-654, 2009.
DOI : 10.1016/j.spa.2008.02.011

URL : http://doi.org/10.1016/j.spa.2008.02.011

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

B. Bouchard, R. Elie, and C. Imbert, Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol.48, issue.5, 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

P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, 2004.

A. Cern-`-cern-`-y and J. Kallsen, On the structure of general mean-variance hedging strategies. The Annals of probability, pp.1479-1531, 2007.

A. Cern-`-cern-`-y and J. Kallsen, Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation, SSRN Electronic Journal, vol.18, issue.3, pp.473-492, 2008.
DOI : 10.2139/ssrn.909305

L. Clewlow and C. Strickland, Energy derivatives: pricing and risk management, Lacima publications Warwick, 2000.

R. Cont and P. Tankov, Financial modelling with jump processes, 2004.
DOI : 10.1201/9780203485217

URL : https://hal.archives-ouvertes.fr/hal-00002693

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

R. Cont, P. Tankov, and E. Voltchkova, Hedging with options in models with jumps. Stochastic analysis and applications, pp.197-217, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00705960

M. 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, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

S. Crépey and A. Matoussi, Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison, The Annals of Applied Probability, vol.18, issue.5, pp.2041-2069, 2008.
DOI : 10.1214/08-AAP517

I. Csiszar, On topological properties of f-divergences, Studia Sci. Math. Hungarica, vol.2, pp.329-339, 1967.

D. Franco, C. , and P. Tankov, Portfolio insurance under a risk-measure constraint, Insurance: Mathematics and Economics, vol.49, issue.3, pp.361-370, 2011.
DOI : 10.1016/j.insmatheco.2011.05.009

URL : https://hal.archives-ouvertes.fr/hal-00705972

D. Franco, C. , P. Tankov, and X. Warin, Quadratic hedge in electricity markets, 2012.

F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer et al., Exponential Hedging and Entropic Penalties, Mathematical Finance, vol.23, issue.2, pp.99-123, 2002.
DOI : 10.1111/1467-9965.00093

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.9442

C. Doléans-dade, Quelques applications de la formule de changement de variables pour les semimartingales, Probability Theory and Related Fields, vol.16, issue.3, pp.181-194, 1970.

J. Doob, Measure theory, 1994.
DOI : 10.1007/978-1-4612-0877-8

I. Ekeland, A. Galichon, and M. Henry, Comonotonic measures of multivariate risks, Mathematical Finance, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01053550

I. Ekeland and W. Schachermayer, Law invariant risk measures on R n, 2011.

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. , 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

E. Karoui, N. , and R. Rouge, Pricing via utility maximization and entropy, Mathematical Finance, vol.10, issue.2, pp.259-276, 2000.

S. Emmer, C. Klüppelberg, and R. Korn, Optimal Portfolios with Bounded Capital at Risk, Mathematical Finance, vol.11, issue.4, pp.365-384, 2001.
DOI : 10.1111/1467-9965.00121

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.147.879

H. Föllmer and P. Leukert, Quantile hedging, Finance and Stochastics, vol.3, issue.3, pp.251-273, 1999.
DOI : 10.1007/s007800050062

H. Föllmer and A. Schied, Stochastic finance. an introduction in discrete time, de Gruyter Studies in Mathematics, vol.648, 2004.

P. Forsyth, Y. Halluin, and K. Vetzal, Robust numerical methods for contingent claims under jump diffusion processes, IMA Journal of Numerical Analysis, vol.25, issue.1, pp.87-112, 2005.

P. Forsyth and G. Labahn, Numerical methods for controlled hamiltonjacobi-bellman pdes in finance, Journal of Computational Finance, vol.11, issue.2, 2007.

P. Forsyth, J. Wan, and I. Wang, Robust numerical valuation of european and american options under the cgmy process, Journal of Computational Finance, vol.10, issue.4, p.31, 2007.

A. Friedman, Partial differential equations of parabolic type, 1964.

M. Frittelli and E. Gianin, Dynamic convex risk measures. Risk measures for the 21st century, pp.227-248, 2004.

L. Galtchouk, Représentation des martingales engendrées par un processusà processusà accroissements indépendants (cas des martingales de carré intégrable), Annales de Henri Poincaré (B), vol.12, pp.199-211, 1976.

H. Geman and A. Roncoroni, Understanding the Fine Structure of Electricity Prices*, The Journal of Business, vol.79, issue.3, 2006.
DOI : 10.1086/500675

URL : https://hal.archives-ouvertes.fr/halshs-00144198

D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, 2001.

A. Gundel and S. Weber, Robust utility maximization with limited downside risk in incomplete markets, Stochastic Processes and Their Applications, pp.1663-1688, 2007.
DOI : 10.1016/j.spa.2007.03.014

X. He and X. Zhou, PORTFOLIO CHOICE VIA QUANTILES, Mathematical Finance, vol.55, issue.1, 2010.
DOI : 10.1111/j.1467-9965.2010.00432.x

F. Hubalek, J. Kallsen, and L. Krawczyk, Variance-optimal hedging for processes with stationary independent increments, The Annals of Applied Probability, vol.16, issue.2, pp.853-885, 2006.
DOI : 10.1214/105051606000000178

H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's, Communications on Pure and Applied Mathematics, vol.56, issue.1, pp.15-45, 1989.
DOI : 10.1002/cpa.3160420103

J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, 2003.
DOI : 10.1007/978-3-662-02514-7

E. Jakobsen and K. Karlsen, Continuous dependence estimates for viscosity solutions of integro-PDEs, Journal of Differential Equations, vol.212, issue.2, pp.278-318, 2005.
DOI : 10.1016/j.jde.2004.06.021

E. Jakobsen and K. Karlsen, A ???maximum principle for semicontinuous functions??? applicable to integro-partial differential equations, Nonlinear Differential Equations and Applications NoDEA, vol.13, issue.2, pp.137-165, 2006.
DOI : 10.1007/s00030-005-0031-6

M. Jeanblanc, M. Mania, M. Santacroce, and M. Schweizer, Mean-Variance Hedging via Stochastic Control and BSDEs for General Semimartingales, 2011.

R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Archive for Rational Mechanics and Analysis, vol.74, issue.1, pp.1-27, 1988.
DOI : 10.1007/BF00281780

H. Jin and X. Y. Zhou, BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME, Mathematical Finance, vol.42, issue.3, p.385, 2008.
DOI : 10.1111/j.1467-9965.2008.00339.x

E. Jouini, M. Meddeb, and N. Touzi, Vector-valued coherent risk measures, Finance and Stochastics, vol.8, issue.4, pp.531-552, 2004.
URL : https://hal.archives-ouvertes.fr/halshs-00167154

E. Jouini, W. Schachermayer, and N. Touzi, Law invariant risk measures have the fatou property Advances in mathematical economics, pp.49-71, 2006.

M. Kaina and L. Rüschendorf, On convex risk measures on L p -spaces, Mathematical Methods of Operations Research, vol.26, issue.3, pp.475-495, 2009.
DOI : 10.1007/s00186-008-0248-3

J. Kallsen and R. Vierthauer, Quadratic hedging in affine stochastic volatility models, Review of Derivatives Research, vol.51, issue.4, pp.3-27, 2009.
DOI : 10.1007/s11147-009-9034-5

I. Karatzas and S. Shreve, Methods of mathematical finance, 1998.

H. Kunita and S. Watanabe, On Square Integrable Martingales, Nagoya Mathematical Journal, vol.30, pp.209-245, 1967.
DOI : 10.1017/S0027763000012484

O. Ladyzenskaja, V. Solonnikov, and N. Ural-'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol.23, 1967.

J. Laurent and H. Pham, Dynamic programming and mean-variance hedging, Finance and Stochastics, vol.3, issue.1, pp.83-110, 1999.
DOI : 10.1007/s007800050053

P. Lions, Optimal control of diffusion processes and hamilton???jacobi???bellman equations part 2 : viscosity solutions and uniqueness, Communications in Partial Differential Equations, vol.25, issue.11, pp.1229-1276, 1983.
DOI : 10.1080/03605308308820301

T. Meyer-brandis and P. Tankov, MULTI-FACTOR JUMP-DIFFUSION MODELS OF ELECTRICITY PRICES, International Journal of Theoretical and Applied Finance, vol.11, issue.05, pp.503-528, 2008.
DOI : 10.1142/S0219024908004907

URL : https://hal.archives-ouvertes.fr/hal-00184563

R. Mikulevicius and H. Pragarauskas, On Hölder solutions of the integrodifferential Zakai equation, Stochastic Processes and their Applications, 2009.

R. Mikulevicius and H. Pragarauskas, On the cauchy problem for integro differential operators in Hölder classes and the uniqueness of the martingale problem. preprint, 2011.

H. Pham, Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, Journal of Mathematical Systems, Estimation and Control, vol.8, issue.1, pp.1-27, 1998.

H. Pham, On quadratic hedging in continuous time, Mathematical Methods of Operations Research (ZOR), vol.51, issue.2, pp.315-339, 2000.
DOI : 10.1007/s001860050091

H. Pham, Optimisation et contrôle stochastique appliquésappliquésà la finance, 2007.

P. Protter, Stochastic integration and differential equations, 2004.

R. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, The Journal of Risk, vol.2, issue.3, pp.21-42, 2000.
DOI : 10.21314/JOR.2000.038

L. Rogers, Optimal and robust contracts for a risk-constrained principal, Mathematics and Financial Economics, vol.21, issue.3, pp.151-171, 2009.
DOI : 10.1007/s11579-009-0018-x

S. Rong, On solutions of backward stochastic differential equations with jumps and applications, Stochastic Processes and their Applications, pp.209-236, 1997.
DOI : 10.1016/S0304-4149(96)00120-2

M. Royer, Backward stochastic differential equations with jumps and related non-linear expectations. Stochastic processes and their applications, pp.1358-1376, 2006.

K. Sato, Lévy processes and infinitely divisible distributions, 1999.

M. Schweizer, A Guided Tour through Quadratic Hedging Approaches, In: Option Pricing, Interest Rates and Risk Management Cvitanic J and Musiela M, pp.538-574, 2001.
DOI : 10.1017/CBO9780511569708.016

H. Triebel, Theory of function spaces II. Modern Birkhäuser Classics, 1992.