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Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming

Citations

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Cited by:

  1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
  2. Manon Costa & Sébastien Gadat & Lorick Huang, 2025. "CV@R penalized portfolio optimization with biased stochastic mirror descent," Post-Print hal-05147991, HAL.
  3. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
  4. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
  5. Dimitris Bertsimas & Xuan Vinh Doan & Karthik Natarajan & Chung-Piaw Teo, 2010. "Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 580-602, August.
  6. Geissel Sebastian & Sass Jörn & Seifried Frank Thomas, 2018. "Optimal expected utility risk measures," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 73-87, January.
  7. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
  8. Samuel Drapeau & Michael Kupper & Antonis Papapantoleon, 2012. "A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents," Papers 1212.6732, arXiv.org, revised Dec 2013.
  9. Louis Raymond Eeckhoudt & Elisa Pagani & Emanuela Rosazza Gianin, 2016. "Prudence, risk measures and the Optimized Certainty Equivalent: a note," Working Papers 07/2016, University of Verona, Department of Economics.
  10. Sumedh Gupte & Prashanth L. A. & Sanjay P. Bhat, 2025. "Gradient-based Stochastic Optimization of Utility-based Shortfall Risk," Papers 2506.01101, arXiv.org, revised Jun 2026.
  11. Gong, Linguo & Sun, Bruce, 1998. "Measuring production with random inputs and outputs using DEA and certainty equivalent," European Journal of Operational Research, Elsevier, vol. 111(1), pages 62-74, November.
  12. Daniel Bartl & Samuel Drapeau & Jan Obloj & Johannes Wiesel, 2020. "Sensitivity analysis of Wasserstein distributionally robust optimization problems," Papers 2006.12022, arXiv.org, revised Nov 2021.
  13. Guanyu Jin & Roger J. A. Laeven & Dick den Hertog, 2025. "Robust Optimization of Rank-Dependent Models with Uncertain Probabilities," Papers 2502.11780, arXiv.org, revised Apr 2025.
  14. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and its application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org, revised Oct 2025.
  15. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
  16. Leonardo Baggiani & Martin Herdegen & Nazem Khan, 2025. "The Interplay between Utility and Risk in Portfolio Selection," Papers 2509.10351, arXiv.org.
  17. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
  18. Jinwook Lee & András Prékopa, 2013. "Properties and calculation of multivariate risk measures: MVaR and MCVaR," Annals of Operations Research, Springer, vol. 211(1), pages 225-254, December.
  19. Martin Herdegen & Nazem Khan, 2025. "ρ -Arbitrage and ρ -Consistent Pricing for Star-Shaped Risk Measures," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1555-1583, May.
  20. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775, arXiv.org.
  21. Daniel Lacker, 2015. "Law invariant risk measures and information divergences," Papers 1510.07030, arXiv.org, revised Jun 2016.
  22. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.
  23. Xiaochuan Deng & Fei Sun, 2019. "Regulator-based risk statistics for portfolios," Papers 1904.08829, arXiv.org, revised Jun 2020.
  24. Çağin Ararat & Andreas H. Hamel & Birgit Rudloff, 2017. "Set-Valued Shortfall And Divergence Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-48, August.
  25. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
  26. Daniel Bartl & Ludovic Tangpi, 2020. "Non-asymptotic convergence rates for the plug-in estimation of risk measures," Papers 2003.10479, arXiv.org, revised Oct 2022.
  27. Darlington, J. & Pantelides, C. C. & Rustem, B. & Tanyi, B. A., 2000. "Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 121(2), pages 343-362, March.
  28. Mucahit Aygun & Roger J. A. Laeven & Mitja Stadje, 2025. "Higher-Order Ambiguity Attitudes," Papers 2501.13143, arXiv.org.
  29. Daniel Bartl & Ludovic Tangpi, 2023. "Nonasymptotic Convergence Rates for the Plug-in Estimation of Risk Measures," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 2129-2155, November.
  30. Arai, Takuji & Asano, Takao & Nishide, Katsumasa, 2019. "Optimal initial capital induced by the optimized certainty equivalent," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 115-125.
  31. Rashed Khanjani-Shiraz & Ali Babapour-Azar & Zohreh Hosseini-Noudeh & Panos M. Pardalos, 2022. "Distributionally robust maximum probability shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 140-167, January.
  32. Fei Sun & Jingchao Li & Jieming Zhou, 2018. "Dynamic risk measures for fluctuations in market volatility under Bochner-Lebesgue spaces," Papers 1806.01166, arXiv.org, revised Jan 2026.
  33. Gong, Linguo & Sun, Bruce, 1995. "Efficiency measurement of production operations under uncertainty," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 55-66, April.
  34. Martin Herdegen & Nazem Khan & Cosimo Munari, 2024. "Risk, utility and sensitivity to large losses," Papers 2405.12154, arXiv.org.
  35. Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised May 2024.
  36. Alessandro Doldi & Marco Frittelli, 2020. "Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality," Papers 2005.12572, arXiv.org, revised Sep 2021.
  37. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
  38. Laeven, R.J.A. & Stadje, M.A., 2011. "Entropy Coherent and Entropy Convex Measures of Risk," Discussion Paper 2011-031, Tilburg University, Center for Economic Research.
  39. Bercu, Bernard & Costa, Manon & Gadat, Sébastien, 2020. "Stochastic approximation algorithms for superquantiles estimation," TSE Working Papers 20-1142, Toulouse School of Economics (TSE).
  40. Jinwook Lee & András Prékopa, 2015. "Decision-making from a risk assessment perspective for Corporate Mergers and Acquisitions," Computational Management Science, Springer, vol. 12(2), pages 243-266, April.
  41. Lacker Daniel, 2018. "Law invariant risk measures and information divergences," Dependence Modeling, De Gruyter, vol. 6(1), pages 228-258, November.
  42. Roger J. A. Laeven & Matteo Ferrari & Emanuela Rosazza Gianin & Marco Zullino, 2025. "Measuring Financial Resilience Using Backward Stochastic Differential Equations," Papers 2505.07502, arXiv.org, revised Jan 2026.
  43. Babacar Seck & Laetitia Andrieu & Michel De Lara, 2012. "Parametric multi-attribute utility functions for optimal profit under risk constraints," Theory and Decision, Springer, vol. 72(2), pages 257-271, February.
  44. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
  45. Roger J. A. Laeven & Mitja Stadje, 2013. "Entropy Coherent and Entropy Convex Measures of Risk," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 265-293, May.
  46. Xiaolei He & Weiguo Zhang, 2025. "An Efficient Scenario Reduction Method for Problems with Higher Moment Coherent Risk Measures," INFORMS Journal on Computing, INFORMS, vol. 37(3), pages 743-760, May.
  47. Radu Boţ & Alina-Ramona Frătean, 2011. "Looking for appropriate qualification conditions for subdifferential formulae and dual representations for convex risk measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 191-215, October.
  48. Cheridito, Patrick & Horst, Ulrich & Kupper, Michael & Pirvu, Traian A., 2011. "Equilibrium pricing in incomplete markets under translation invariant preferences," SFB 649 Discussion Papers 2011-083, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  49. repec:hal:journl:hal-03610477 is not listed on IDEAS
  50. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
  51. Mucahit Aygun & Fabio Bellini & Roger J. A. Laeven, 2023. "Elicitability of Return Risk Measures," Papers 2302.13070, arXiv.org, revised Mar 2023.
  52. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
  53. Prékopa, András & Lee, Jinwook, 2018. "Risk tomography," European Journal of Operational Research, Elsevier, vol. 265(1), pages 149-168.
  54. Yining Gu & Yicheng Huang & Yanjun Wang, 2024. "Data-Driven Distributionally Robust Risk-Averse Two-Stage Stochastic Linear Programming over Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 242-279, January.
  55. Zhenfeng Zou, 2026. "Generalized Optimal Initial Capital and Risk Measures Induced by the Generalized Certainty Equivalent," Methodology and Computing in Applied Probability, Springer, vol. 28(1), pages 1-24, March.
  56. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2017. "Computational aspects of robust optimized certainty equivalents and option pricing," Papers 1706.10186, arXiv.org, revised Mar 2019.
  57. Costa, Manon & Gadat, Sébastien & Huang, Lorick, 2022. "CV@R penalized portfolio optimization with biased stochastic mirror descent," TSE Working Papers 22-1342, Toulouse School of Economics (TSE), revised Nov 2023.
  58. Liu, Kanglin & Li, Qiaofeng & Zhang, Zhi-Hai, 2019. "Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 79-101.
  59. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
  60. Gadat, Sébastien & Costa, Manon, 2020. "Non asymptotic controls on a stochastic algorithm for superquantile approximation," TSE Working Papers 20-1149, Toulouse School of Economics (TSE).
  61. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
  62. Giulio Principi & Fabio Maccheroni, 2022. "Conditional divergence risk measures," Papers 2211.04592, arXiv.org.
  63. Zhang, Tao & Wang, Shuaian & Xin, Xu, 2025. "Liner fleet deployment and slot allocation problem: A distributionally robust optimization model with joint chance constraints," Transportation Research Part B: Methodological, Elsevier, vol. 197(C).
  64. Manon Costa & Sébastien Gadat & Lorick Huang, 2025. "CV@R-penalised portfolio optimisation with biased stochastic mirror descent," Finance and Stochastics, Springer, vol. 29(3), pages 609-664, July.
  65. c{C}au{g}{i}n Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org, revised Sep 2017.
  66. Drew P. Kouri & Thomas M. Surowiec, 2020. "Epi-Regularization of Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 774-795, May.
  67. Mucahit Aygun & Fabio Bellini & Roger J. A. Laeven, 2025. "Generalized Orlicz premia," Papers 2507.09181, arXiv.org.
  68. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.
  69. Zachary J. Smith & J. Eric Bickel, 2022. "Weighted Scoring Rules and Convex Risk Measures," Operations Research, INFORMS, vol. 70(6), pages 3371-3385, November.
  70. Adi Ben-Israel & Aharon Ben-Tal, 1997. "Duality and equilibrium prices in economics of uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(1), pages 51-85, February.
  71. Zhongde Luo, 2020. "Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences," Statistical Papers, Springer, vol. 61(2), pages 615-643, April.
  72. Daniel Lacker, 2015. "Liquidity, risk measures, and concentration of measure," Papers 1510.07033, arXiv.org, revised Oct 2015.
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