References
- Merton RC. Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econ. Stat. 1969;51:247–257.
- Kramkov D, Schachermayer W. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 1999;9:904–950.
- Kramkov D, Schachermayer W. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 2003;13:1504–1516.
- Artzner P, Delbaen F, Eber J-M, et al. Coherent measures of risk. Math. Finance. 1999;9:203–228.
- Föllmer H, Schied A. Convex measures of risk and trading. Finance Stochastics. 2002;6:429–447.
- Leibowitz ML, Henriksson RD. Portfolio Optimization with Shortfall Constraints: A Confidence-Limit Approach to Managing Downside Risk. Financial Analysts J. 1989;45:34–41.
- Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. J. Risk. 2000;2:21–41.
- Acerbi C, Tasche D. Expected shortfall: a natural coherent alternative to value at risk. Economic Notes by Banca Monte dei Paschi di Siena SpA. 2002;31:379–388.
- Bertsimas D, Laprete GJ, Samarov A. Shortfall as a risk measure: properties, optimization and applications. J. Econ. Dyn. Control. 2004;28:1353–1381.
- Goldberg LR, Hayes MY, Mahmoud O. Minimizing shortfall. Quant. Finance. 2013;13:1533–1545.
- Bin L. A new risk measure and its application in portfolio optimization: the SPP-CVaR approach. Econ. Model. 2015;51:383–390.
- Karatzas I, Lehoczky JP, Shreve SE. Optimal portfolio and consumption decisions for a “small Investor” on a finite horizon. SIAM J. Control Optim. 1987;25:1557–1586.
- Karatzas I, Zitkovic G. Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 2003;31:1821–1858.
- Basak S, Shapiro A. Value-at-risk-based risk management: optimal policies and asset prices. Rev. Financial Stud. 2001;14:371–405.
- Gabih A, Wunderlich R. Optimal portfolios with bounded shortfall risks. In vom Scheidt J, editor. Proceedings of the workshop Stochastic Analysis. Chemnitz: Technische Universität, Faculty of Mathematics; 2004. pp. 21–41.
- Gabih A, Grecksch W, Wunderlich R. Dynamic portfolio optimization with bounded shortfall risks. Stochastic Anal. Appl. 2005;3:579–594.
- Gundel A, Weber S. Robust utility maximization with limited downside risk in incomplete markets. Stochastic Processes Appl. 2007;117:1663–1688.
- Gundel A, Weber S. Utility maximization under a shortfall risk constraint. J. Math. Econ. 2008;44:1126–1151.
- Gabih A, Sass J, Wunderlich R. Utility maximization under bounded expected loss. Stochastic Models. 2009;25: 375–407.
- Rudloff B, Sass J, Wunderlich R. Entropic risk constraints for utility maximization. In Tammer C, Heyde F, editors. Festschrift in Celebration of Prof. Dr. Wilfried Grecksch’s 60th Birthday. Aachen: Shaker Verlag; 2008. pp. 149–180.
- Moreno-Bromberg S, Pirvu TA, Réveillac A. CRRA Utility Maximization under Risk Constraints. Commun. Stochastic Anal. 2013;7:203–225.
- Horst U, Pirvu TA, Dos Reis G. On securitization, market completion and equilibrium risk transfer. Math. Financial Econ. 2010;2:211–252.
- Backhoff J, Silva FJ. Some sensitive results in stochastic optimal control: a Lagrange multiplier point of view. 2015. Forthcoming.
- Cuoco D, He H, Isaenko S. Optimal dynamic trading strategies with risk limits. Oper. Res. 2008;56:358–368.
- Gabih A. Portfolio optimization with bounded shortfall risks dissertation. Halle-Wittenberg: Martin-Luther-Universität; 2005.
- Delbaen F, Schachermayer W. A general version of the fundamental theorem of asset pricing. Math. Ann. 1994;300:463–520.
- Kardaras C, Platen E. On the semimartingale property of discounted asset price processes. Stochastic Processes and their Applications. 2011;121:2678–2691.
- Karatzas I, Lehoczky JP, Shreve SE, et al. Martingale and duality methods for utility maximization in an incomplete market. SIAM J. Control Optim. 1991;29:702–730.
- Rockafellar RT. Convex analysis. Princeton: Princeton University Press; 1970.
- Giesecke K, Schmidt T, Weber S. Measuring the risk of large losses. J. Investment Manage. 2008;6:1–15.
- Weber S. Distribution-invariant risk measures, information, and dynamic consistency. Mathematical Finance. 2006;16:419–442.
- Bellini F, Bignozzi V. On elicitable risk measures. Quant. Finance. 2015;15:725–733.
- Newey WK, Powell JL. Asymmetric least squares estimation and testing. Econometrica. 1987;55:819–847.
- Delbaen F, Bellini F, Bignozzi V, et al. Risk measures with the CxLS property. Finance Stochastics. 2016;20:433–453.