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Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices

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Cited by:

  1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
  2. Leonard C. MacLean & Yonggan Zhao & William T. Ziemba, 2016. "Optimal capital growth with convex shortfall penalties," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 101-117, January.
  3. Escobar-Anel, Marcos & Havrylenko, Yevhen & Kschonnek, Michel & Zagst, Rudi, 2022. "Decrease of capital guarantees in life insurance products: Can reinsurance stop it?," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 14-40.
  4. Jianjun Gao & Ke Zhou & Duan Li & Xiren Cao, 2014. "Dynamic Mean-LPM and Mean-CVaR Portfolio Optimization in Continuous-time," Papers 1402.3464, arXiv.org.
  5. Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.
  6. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
  7. Donatien Hainaut, 2009. "Dynamic asset allocation under VaR constraint with stochastic interest rates," Annals of Operations Research, Springer, vol. 172(1), pages 97-117, November.
  8. Ke Zhou & Jiangjun Gao & Duan Li & Xiangyu Cui, 2017. "Dynamic mean–VaR portfolio selection in continuous time," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1631-1643, October.
  9. Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
  10. Juan Carlos Escanciano & Zaichao Du, 2015. "Backtesting Expected Shortfall: Accounting for Tail Risk," CAEPR Working Papers 2015-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
  11. Wanbing Zhang & Sisi Zhang & Peibiao Zhao, 2019. "On Double Value at Risk," Risks, MDPI, vol. 7(1), pages 1-22, March.
  12. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
  13. Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
  14. Liu, Zhimin & Qu, Shaojian & Goh, Mark & Wu, Zhong & Huang, Ripeng & Ma, Gang, 2020. "Two-stage mean-risk stochastic optimization model for port cold storage capacity under pelagic fishery yield uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
  15. Hirbod Assa & Peng Liu, 2024. "Factor risk measures," Papers 2404.08475, arXiv.org.
  16. Mark Carey & René M. Stulz, 2007. "The Risks of Financial Institutions," NBER Books, National Bureau of Economic Research, Inc, number care06-1.
  17. Boon, L.N. & Brière, M. & Rigot, S., 2018. "Regulation and pension fund risk-taking," Journal of International Money and Finance, Elsevier, vol. 84(C), pages 23-41.
  18. Wong, Woon K., 2010. "Backtesting value-at-risk based on tail losses," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 526-538, June.
  19. Dennis Frestad & Fred Espen Benth & Steen Koekebakker, 2010. "Modeling Term Structure Dynamics in the Nordic Electricity Swap Market," The Energy Journal, , vol. 31(2), pages 53-86, April.
  20. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
  21. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
  22. Bayraktar, Erhan & Young, Virginia R., 2008. "Maximizing utility of consumption subject to a constraint on the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(4), pages 204-212, December.
  23. Christophe Boucher & Benjamin Hamidi & Patrick Kouontchou & Bertrand Maillet, 2012. "Une évaluation économique du risque de modèle pour les investisseurs de long terme," Revue économique, Presses de Sciences-Po, vol. 63(3), pages 591-600.
  24. Timotheos Angelidis & Alexandros Benos, 2008. "Value-at-Risk for Greek Stocks," Multinational Finance Journal, Multinational Finance Journal, vol. 12(1-2), pages 67-104, March-Jun.
  25. Sarafrazi, Soodabeh & Hammoudeh, Shawkat & AraújoSantos, Paulo, 2014. "Downside risk, portfolio diversification and the financial crisis in the euro-zone," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 32(C), pages 368-396.
  26. Yao, Jing & Li, Duan, 2013. "Bounded rationality as a source of loss aversion and optimism: A study of psychological adaptation under incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 18-31.
  27. Zhen Shi & Bas J.M. Werker, 2011. "Economic Costs and Benefits of Imposing Short-Horizon Value-at-Risk Type Regulation," Tinbergen Institute Discussion Papers 11-053/2/DSF17, Tinbergen Institute.
  28. Jón Daníelsson & Bjørn N. Jorgensen & Casper G. de Vries & Xiaogang Yang, 2001. "Optimal Portfolio Allocation under a Probabilistic Risk Constraint and the Incentives for Financial Innovation," Tinbergen Institute Discussion Papers 01-069/2, Tinbergen Institute.
  29. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
  30. Daniel Bauer & George Zanjani, 2016. "The Marginal Cost of Risk, Risk Measures, and Capital Allocation," Management Science, INFORMS, vol. 62(5), pages 1431-1457, May.
  31. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
  32. Fermanian, Jean-David & Scaillet, Olivier, 2005. "Sensitivity analysis of VaR and Expected Shortfall for portfolios under netting agreements," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 927-958, April.
  33. Christiane Baumeister & Lutz Kilian, 2014. "Real-Time Analysis of Oil Price Risks Using Forecast Scenarios," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 62(1), pages 119-145, April.
  34. De Franco, Carmine & Tankov, Peter, 2011. "Portfolio insurance under a risk-measure constraint," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 361-370.
  35. Lutz Kilian & Simone Manganelli, 2008. "The Central Banker as a Risk Manager: Estimating the Federal Reserve's Preferences under Greenspan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(6), pages 1103-1129, September.
  36. Traian A. Pirvu & Gordan Žitković, 2009. "Maximizing The Growth Rate Under Risk Constraints," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 423-455, July.
  37. Benjamin Avanzi & Hayden Lau & Mogens Steffensen, 2022. "Optimal reinsurance design under solvency constraints," Papers 2203.16108, arXiv.org, revised Jun 2023.
  38. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, March.
  39. Bertrand, Philippe & Prigent, Jean-luc, 2016. "Equilibrium of financial derivative markets under portfolio insurance constraints," Economic Modelling, Elsevier, vol. 52(PA), pages 278-291.
  40. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
  41. Mei Choi Chiu & Hoi Ying Wong & Duan Li, 2012. "Roy’s Safety‐First Portfolio Principle in Financial Risk Management of Disastrous Events," Risk Analysis, John Wiley & Sons, vol. 32(11), pages 1856-1872, November.
  42. Trindade, A. Alexandre & Uryasev, Stan & Shapiro, Alexander & Zrazhevsky, Grigory, 2007. "Financial prediction with constrained tail risk," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3524-3538, November.
  43. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
  44. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
  45. Patra, Pradipta & Kumar, U. Dinesh & Nowicki, David R. & Randall, Wesley S., 2019. "Effective management of performance-based contracts for sustainment dominant systems," International Journal of Production Economics, Elsevier, vol. 208(C), pages 369-382.
  46. Ji Cao, 2017. "How does the underlying affect the risk-return profiles of structured products?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(1), pages 27-47, February.
  47. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
  48. Bahrs, E., 2001. "Methoden des Rechnungswesens als Instrumente des Risikomanagements in der Landwirtschaft," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 37.
  49. Chabakauri, Georgy & Han, Brandon Yueyang, 2020. "Collateral constraints and asset prices," Journal of Financial Economics, Elsevier, vol. 138(3), pages 754-776.
  50. Christian Gourieroux & Wei Liu, 2006. "Efficient Portfolio Analysis Using Distortion Risk Measures," Working Papers 2006-17, Center for Research in Economics and Statistics.
  51. Zhang, Qingye & Gao, Yan, 2016. "Optimal consumption—portfolio problem with CVaR constraints," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 516-521.
  52. Arouri, Mohamed & M’saddek, Oussama & Nguyen, Duc Khuong & Pukthuanthong, Kuntara, 2019. "Cojumps and asset allocation in international equity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 1-22.
  53. Jianming Xia, 2021. "Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures," Papers 2112.02284, arXiv.org.
  54. Bryan R. Routledge & Stanley E. Zin, 2010. "Generalized Disappointment Aversion and Asset Prices," Journal of Finance, American Finance Association, vol. 65(4), pages 1303-1332, August.
  55. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  56. José Santiago Fajardo Barbachan & Aquiles Rocha de Farias & José Renato Haas Ornelas, 2008. "A Goodness-of-Fit Test with Focus on Conditional Value at Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 6(2), pages 139-155.
  57. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
  58. Philippe Jorion, 2007. "Bank Trading Risk and Systemic Risk," NBER Chapters, in: The Risks of Financial Institutions, pages 29-57, National Bureau of Economic Research, Inc.
  59. Jón Daníelsson & Jean-Pierre Zigrand, 2008. "Equilibrium asset pricing with systemic risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 293-319, May.
  60. Leonard Arvi & Herman Manakyan & Kashi Khazeh, 2023. "Estimated Impact of Covid-19 on Exchange Rate Risk of Multinational Enterprises Operating in Emerging Markets," International Journal of Economics and Financial Issues, Econjournals, vol. 13(4), pages 23-29, July.
  61. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
  62. de Jong, Frank, 2008. "Pension fund investments and the valuation of liabilities under conditional indexation," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 1-13, February.
  63. Manganelli, Simone, 2007. "Asset allocation by penalized least squares," Working Paper Series 723, European Central Bank.
  64. Lawrence Haar & Andros Gregoriou, 2023. "Regulation and De-Risking: Theoretical and Empirical Insights," Risks, MDPI, vol. 11(6), pages 1-23, June.
  65. Alquist, Ron & Kilian, Lutz & Vigfusson, Robert J., 2013. "Forecasting the Price of Oil," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 427-507, Elsevier.
  66. Holod, Dmytro & Kitsul, Yuriy & Torna, Gökhan, 2020. "Market risk-based capital requirements, trading activity, and bank risk," Journal of Banking & Finance, Elsevier, vol. 112(C).
  67. Yalcin Akcay & Atakan Yalcin, 2010. "Optimal Portfolio Selection With A Shortfall Probability Constraint: Evidence From Alternative Distribution Functions," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 33(1), pages 77-102, March.
  68. José Vicente & Aloísio Araújo, 2010. "Social Welfare Analysis in a Financial Economy with Risk Regulation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(3), pages 561-586, June.
  69. Huang, Jinbo & Ding, Ashley & Li, Yong & Lu, Dong, 2020. "Increasing the risk management effectiveness from higher accuracy: A novel non-parametric method," Pacific-Basin Finance Journal, Elsevier, vol. 62(C).
  70. B'enamar Chouaf & Serguei Pergamenchtchikov, 2010. "Optimal investment with bounded VaR for power utility functions," Papers 1002.3681, arXiv.org, revised Feb 2010.
  71. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.
  72. Christoffersen, Peter & Langlois, Hugues, 2013. "The Joint Dynamics of Equity Market Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(5), pages 1371-1404, October.
  73. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
  74. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
  75. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
  76. Solange M. Berstein & Rómulo A. Chumacero, 2012. "VaR limits for pension funds: an evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1315-1324, May.
  77. Weiping Wu & Yu Lin & Jianjun Gao & Ke Zhou, 2023. "Mean-variance hybrid portfolio optimization with quantile-based risk measure," Papers 2303.15830, arXiv.org, revised Apr 2023.
  78. Wong, Woon K & Copeland, Laurence, 2008. "Risk Measurement and Management in a Crisis-Prone World," Cardiff Economics Working Papers E2008/14, Cardiff University, Cardiff Business School, Economics Section.
  79. Bernard, Carole & Cui, Xuecan, 2023. "Impact of systemic risk regulation on optimal policies and asset prices," Journal of Banking & Finance, Elsevier, vol. 154(C).
  80. Constantin Mellios & Anh Ngoc Lai, 2022. "Incentive Fees with a Moving Benchmark and Portfolio Selection under Loss Aversion," Post-Print hal-03708926, HAL.
  81. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
  82. Tak Siu, 2012. "A BSDE approach to risk-based asset allocation of pension funds with regime switching," Annals of Operations Research, Springer, vol. 201(1), pages 449-473, December.
  83. Jang, Bong-Gyu & Park, Seyoung, 2016. "Ambiguity and optimal portfolio choice with Value-at-Risk constraint," Finance Research Letters, Elsevier, vol. 18(C), pages 158-176.
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  85. Tu, Anthony H. & Chen, Cathy Yi-Hsuan, 2018. "A factor-based approach of bond portfolio value-at-risk: The informational roles of macroeconomic and financial stress factors," Journal of Empirical Finance, Elsevier, vol. 45(C), pages 243-268.
  86. repec:ipg:wpaper:2014-330 is not listed on IDEAS
  87. Rengifo, Erick W. & Trifan, Emanuela, 2007. "Investors Facing Risk: Loss Aversion and Wealth Allocation Between Risky and Risk-Free Assets," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 28063, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
  88. Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
  89. An Chen & Mitja Stadje & Fangyuan Zhang, 2020. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Papers 2002.02229, arXiv.org, revised Jun 2022.
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  94. Xue Dong He & Hanqing Jin & Xun Yu Zhou, 2015. "Dynamic Portfolio Choice When Risk Is Measured by Weighted VaR," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 773-796, March.
  95. Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Constrained Kelly portfolios under alpha-stable laws," IRTG 1792 Discussion Papers 2019-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
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  97. Alev Meral, 2019. "Comparison of various risk measures for an optimal portfolio," Papers 1912.09573, arXiv.org.
  98. MacLean, Leonard & Zhao, Yonggan & Ziemba, William, 2006. "Dynamic portfolio selection with process control," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 317-339, February.
  99. Ji Cao & Marc Rieger, 2013. "Risk classes for structured products: mathematical aspects and their implications on behavioral investors," Annals of Finance, Springer, vol. 9(2), pages 167-183, May.
  100. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
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  102. Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2022. "Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model," Papers 2208.14152, arXiv.org, revised Jul 2024.
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  118. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, July.
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  121. Marcos Escobar-Anel, 2022. "A dynamic programming approach to path-dependent constrained portfolios," Annals of Operations Research, Springer, vol. 315(1), pages 141-157, August.
  122. Andrea Consiglio & Flavio Cocco & Stavros Zenios, 2007. "Scenario optimization asset and liability modelling for individual investors," Annals of Operations Research, Springer, vol. 152(1), pages 167-191, July.
  123. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
  124. Alejandro Balbás & José Garrido & Silvia Mayoral, 2009. "Properties of Distortion Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 385-399, September.
  125. Lutz Kilian & Simone Manganelli, 2007. "Quantifying the Risk of Deflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2‐3), pages 561-590, March.
  126. Caio Almeida & Kym Ardison & René Garcia & Jose Vicente, 2017. "Nonparametric Tail Risk, Stock Returns, and the Macroeconomy," Journal of Financial Econometrics, Oxford University Press, vol. 15(3), pages 333-376.
  127. Sun, Yufei & Aw, Grace & Teo, Kok Lay & Zhu, Yanjian & Wang, Xiangyu, 2016. "Multi-period portfolio optimization under probabilistic risk measure," Finance Research Letters, Elsevier, vol. 18(C), pages 60-66.
  128. Fardeau, Vincent, 2024. "Arbitrage with financial constraints and market power," Journal of Economic Theory, Elsevier, vol. 217(C).
  129. Panos Kouvelis & Rong Li, 2019. "Integrated Risk Management for Newsvendors with Value-at-Risk Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 816-832, October.
  130. Panageas, Stavros, 2010. "Bailouts, the incentive to manage risk, and financial crises," Journal of Financial Economics, Elsevier, vol. 95(3), pages 296-311, March.
  131. Tahereh Khodamoradi & Maziar Salahi, 2023. "Extended mean-conditional value-at-risk portfolio optimization with PADM and conditional scenario reduction technique," Computational Statistics, Springer, vol. 38(2), pages 1023-1040, June.
  132. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2014. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 59292, London School of Economics and Political Science, LSE Library.
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