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A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LMmeasure perspective
1 Department of Applied Mathematics, Illinois Institute of Technology, 10 W 32 nd Str, Building E1, Room 208, Chicago, IL 60616, USA; 
2 Institute of Mathematics, Jagiellonian University, Cracow, Poland 
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Artzner, P, Delbaen, F, Eber, JM, Heath, D:Coherent measures of risk. Math. Finance 9(3), 203228(1999), 
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Artzner, P, Delbaen, F, Eber, JM, Heath, D, Ku, H:Coherent multiperiod risk measurement. Preprint(2002a), 
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Artzner, P, Delbaen, F, Eber, JM, Heath, D, Ku, H:Coherent multiperiod risk adjusted values and Bellman's principle. Ann. Oper. Res 152, 522 (2007), 
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Barron, EN, Cardaliaguet, P, Jensen, R:Conditional essential suprema with applications. Appl. Math.Optim 48(3), 229253 (2003), 
[8] 
Barrieu, P, El Karoui, N:Optimal derivatives design under dynamic risk measures. Mathematics of finance, volume 351 of Contemp. Math, pp. 1325 (2004). Amer. Math. Soc Barrieu, P, El Karoui, N:Infconvolution of risk measures and optimal risk transfer. Finance Stoch 9(2), 269298 (2005), 
[9] 
Barrieu, P, El Karoui, N:Pricing, hedging and optimally designing derivatives via minimization of risk measures. In:Carmona, R (ed.) Indifference Pricing. Princeton University Press (2007), 
[10] 
Bellman, RE, Dreyfus, SE:Applied dynamic programming. Princeton University Press (1962), 
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Biagini, S, BionNadal, J:Dynamic quasiconcave performance measures. J. Math. Econ 55, 143153(2014), 
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Bielecki, TR, Pliska, SR:Economic properties of the risk sensitive criterion for portfolio management.Rev. Account. Finance 2, 317 (2003), 
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Bielecki, TR, Cialenco, I, Iyigunler, I, Rodriguez, R:Dynamic Conic Finance:Pricing and hedging via dynamic coherent acceptability indices with transaction costs. Int. J. Theor. Appl. Finance 16(01), 1350002 (2013), 
[14] 
Bielecki, TR, Cialenco, I, Pitera, M:A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time. Preprint (2014a), 
[15] 
Bielecki, TR, Cialenco, I, Zhang, Z:Dynamic coherent acceptability indices and their applications to finance. Math. Finance 24(3), 411441 (2014b), 
[16] 
Bielecki, TR, Cialenco, I, Pitera, M:Dynamic limit growth indices in discrete time. Stochastic Models 31, 494523 (2015a), 
[17] 
Bielecki, TR, Cialenco, I, Chen, T:Dynamic conic finance via Backward Stochastic Difference Equations.SIAM J. Finan. Math 6(1), 10681122 (2015b), 
[18] 
Bielecki, TR, Cialenco, I, Drapeau, S, Karliczek, M:Dynamic assessment indices. Stochastics:Int. J.Probab. Stochastic Process 88(1), 144 (2016), 
[19] 
BionNadal, J:Dynamic risk measures:time consistency and risk measures from BMO martingales.Finance Stoch 12(2), 219244 (2008), 
[20] 
BionNadal, J:Bidask dynamic pricing in financial markets with transaction costs and liquidity risk. J.Math. Econ 45(11), 738750 (2009a), 
[21] 
BionNadal, J:Time consistent dynamic risk processes. Stochastic Process. Appl 119(2), 633654 (2009b), 
[22] 
BionNadal, J:Dynamic risk measures and pathdependent second order PDEs. In:Espen Benth, F, Di Nunno, G (eds.) Stochastics of Environmental and Financial Economics, volume 138 of Springer Proceedings in Mathematics & Statistics, pp. 147178. Springer (2016), 
[23] 
Boda, K, Filar, J:Time consistent dynamic risk measures. Math. Methods Oper. Res 63(1), 169186 (2006), 
[24] 
BionNadal, J, Kervarec, M:Dynamic risk measuring under model uncertainty:taking advantage of the hidden probability measure. Preprint (2010), 
[25] 
BionNadal, J, Kervarec, M:Risk measuring under model uncertainty. Ann. App. Prob 1, 213238 (2012), 
[26] 
Carpentier, P, Chancelier, JP, Cohen, G, De Lara, M, Girardeau, P:Dynamic consistency for stochastic optimal control problems. Ann. Oper. Res 200(1), 247263 (2012), 
[27] 
Cheridito, P, Kupper, M:Recursiveness of indifference prices and translationinvariant preferences. Math.Financ. Econ 2(3), 173188 (2009), 
[28] 
Cheridito, P, Kupper, M:Composition of timeconsistent dynamic monetary risk measures in discrete time. Int. J. Theor. Appl. Finance 14(1), 137162 (2011), 
[29] 
Cheridito, P, Li, T:Dual characterization of properties of risk measures on Orlicz hearts. Math. Financ.Econ 2(1), 2955 (2008), 
[30] 
Cheridito, P, Li, T:Risk measures on Orlicz hearts. Math. Finance 19(2), 189214 (2009), 
[31] 
Cherny, A:Weighted V@R and its properties. Finance Stoch 10(3), 367393 (2006), 
[32] 
Cherny, A:Pricing and hedging European options with discretetime coherent risk. Finance Stoch 11(4), 537569 (2007), 
[33] 
Cherny, A:Capital allocation and risk contribution with discretetime coherent risk. Math. Finance 19(1), 1340 (2009), 
[34] 
Cherny, A:Riskreward optimization with discretetime coherent risk. Math. Finance 20(4), 571595(2010), 
[35] 
Cherny, A, Madan, DB:Pricing and hedging in incomplete markets with coherent risk, 21 (2006). https://ssrn.com/abstract=904806, 
[36] 
Cherny, A, Madan, DB:New measures for performance evaluation. Rev. Financial Stud 22(7), 25712606(2009), 
[37] 
Cherny, A, Madan, DB:Markets as a counterparty:An introduction to conic finance. Int. J. Theor. Appl.Finance (IJTAF) 13(08), 11491177 (2010), 
[38] 
Cheridito, P, Delbaen, F, Kupper, M:Dynamic monetary risk measures for bounded discretetime processes. Electron. J. Probab 11(3), 57106 (2006), 
[39] 
Cheridito, P, Stadje, M:Timeinconsistency of VaR and timeconsistent alternatives. Finance Res. Lett 6(1), 4046 (2009), 
[40] 
Cohen, SN, Elliott, RJ:A general theory of finite state backward stochastic difference equations.Stochastic Process. Appl 120(4), 442466 (2010), 
[41] 
Cohen, SN, Elliott, RJ:Backward stochastic difference equations and nearlytimeconsistent nonlinear expectations. SIAM J. Control Optim 49(1), 125139 (2011), 
[42] 
Coquet, F, Hu, Y, Mémin, J, Peng, S:Filtrationconsistent nonlinear expectations and related gxpectations. Probab. Theory Relat. Fields 123(1), 127 (2002), 
[43] 
Davis, M, Lleo, S:RiskSensitive Investment Management, volume 19 of Advanced Series on Statistical Science & Applied Probability. World Sci (2014), 
[44] 
Delbaen, F:Coherent risk measures. Scuola Normale Superiore (2000), 
[45] 
Delbaen, F:Coherent risk measures on general probability spaces. Advances in finance and stochastics, pp. 137. Springer (2002), 
[46] 
Delbaen, F:The structure of mstable sets and in particular of the set of risk neutral measures. In memoriam PaulAndré Meyer:Séminaire de Probabilités XXXIX, volume 1874 of Lecture Notes in Math., pp. 215258. Springer, Berlin (2006), 
[47] 
Delbaen, F:Monetary Utility Functions, volume 3 of CSFI Lecture Notes Series. Osaka University Press(2012), 
[48] 
Delbaen, F, Peng, S, Rosazza Gianin, E:Representation of the penalty term of dynamic concave utilities.Finance Stoch 14, 449472 (2010), 
[49] 
Detlefsen, K, Scandolo, G:Conditional and dynamic convex risk measures. Finance Stochastics 9(4), 539561 (2005), 
[50] 
Drapeau, S:Risk Preferences and their Robust Representation. PhD thesis, Humboldt Universität zu Berlin (2010), 
[51] 
Drapeau, S, Kupper, M:Risk preferences and their robust representation. Math. Oper. Res 38(1), 2862(2013), 
[52] 
Elliott, RJ, Siu, TK, Cohen, SN:Backward stochastic difference equations for dynamic convex risk measures on a binomial tree. J. Appl. Probab 52(3), 2015 (2015), 
[53] 
Epstein, LG, Schneider, M:Recursive multiplepriors. J. Econom. Theory 113(1), 131 (2003), 
[54] 
Fan, J, Ruszczyński, A:Processbased risk measures for observable and partially observable discretetime controlled systems. Preprint (2014), 
[55] 
Fasen, V, Svejda, A:Time consistency of multiperiod distortion measures. Stat. Risk Model 29(2), 133153 (2012), 
[56] 
Feinstein, Z, Rudloff, B:Time consistency of dynamic risk measures in markets with transaction costs.Quant. Finance 13(9), 14731489 (2013), 
[57] 
Feinstein, Z, Rudloff, B:Multiportfolio time consistency for setvalued convex and coherent risk measures. Finance Stochastics 19(1), 67107 (2015), 
[58] 
Filipovic, D, Kupper, M, Vogelpoth, N:Separation and duality in locally L^{0}convex modules. J. Funct.Anal 256, 39964029 (2009), 
[59] 
Frittelli, M, Maggis, M:Conditional certainty equivalent. Int. J. Theor. Appl. Fin 14(1), 4159(2010), 
[60] 
Frittelli, M, Maggis, M:Dual representation of quasiconvex conditional maps. SIAM J. Fin. Math 2, 357382 (2011), 
[61] 
Frittelli, M, Maggis, M:Complete duality for quasiconvex dynamic risk measures on modules of the l^{p}type. Stat. Risk Model 31(1), 103128 (2014), 
[62] 
Frittelli, M, Rosazza Gianin, E:Dynamic convex measures. Risk Measures in 21st Century, G. Szegö ed., pp. 227248 (2004). J. Wiley, 
[63] 
Frittelli, M, Scandolo, G:Risk measures and capital requirements for processes. Math. Finance 16(4), 589612 (2006), 
[64] 
Föllmer, H, Penner, I:Convex risk measures and the dynamics of their penalty functions. Statist. Decis 24(1), 6196 (2006), 
[65] 
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