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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 72, 2023 - Issue 2
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Articles

A new coherent multivariate average-value-at-risk

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Pages 493-519 | Received 12 Sep 2020, Accepted 06 Aug 2021, Published online: 06 Sep 2021

References

  • Artzner P, Delbaen F, Eber JM, et al. Coherent measures of risk. Math Finance. 1999;9:203–228.
  • Shapiro A, Dentcheva D, Ruszczynski A. Lectures on stochastic programming -- modeling and theory. Philadelphia (PA): SIAM; 2009.
  • Pflug G, Romisch W. Modeling, measuring and managing risk. London: World Scientific Publishing Co.; 2007.
  • Follmer H, Schied A. Convex and coherent risk measures. Encycl Quant Finance. 2010;355–363. https://onlinelibrary.wiley.com/doi/full/10.1002/9780470061602.eqf15003
  • Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. J Risk. 2000;2:21–42.
  • Rockafellar RT, Uryasev S. Conditional value-at-risk for general loss distributions. J Bank Finance. 2002;26(7):1443–1471.
  • Cai J, Li H. Conditional tail expectations for multivariate phase-type distributions. J Appl Probab. 2005;42:810–825.
  • Katsuki Y, Matsumoto K. Tail VaR measures in a multi-period setting. Appl Math Finance. 2014;21:270–297.
  • Ogryczak W. Tail mean and related robust solution concepts. Int J Syst Sci. 2014;45:29–38.
  • Ruszczynski A, Shapiro A. Optimization of convex risk functions. Math Oper Res. 2006;31:433–452.
  • Ben-Tal A, Teboulle M. An old-new concept of convex risk measures: the optimized certainty equivalent. Math Fin. 2007;17(3):449–476.
  • Sangaiah AK, Tirkolaee EB, Goli A, et al. Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem. Soft Comput. 2019;24(11):7885–7905.
  • Goli A, Tirkolaee EB, Soltani M. A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors. Prod Manuf Res. 2019;7(1):294–315.
  • Tirkolaee BE, Goli A, Pahlevan M, et al. A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization. Waste Manag Res. 2019;37(11):1089–1101.
  • Goli A, Khademi Zare H, Tavakkoli-Moghaddam R, et al. Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm. Numer Algebra Control Optim. 2019;9(2):187–209.
  • Goli A, Babaee Tirkolaee E, Aydin NS. Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors. IEEE Trans Fuzzy Syst. 2021. published online. https://ieeexplore.ieee.org/document/9333682
  • Goli A, Malmir B. A covering tour approach for disaster relief locating and routing with fuzzy demand. Int J Intel Trans Syst Res. 2019;18(1):140–152.
  • Pahlevan SM, Hosseini SM, Goli A. Sustainable supply chain network design using products' life cycle in the aluminum industry. Environ Sci Pollution Res. 2021. published online. https://link.springer.com/article/10.1007/s11356-020-12150-8
  • Wei L, Hu Y. Coherent and convex risk measures for portfolios with applications. Stat Probab Lett. 2014;90:114–120.
  • Burgert C, Ruschendorf L. Consistent risk measures for portfolio vectors. Insure Math Econom. 2006;38:289–297.
  • Hamel A, Rudloff B, Yankova M. Set-valued average value at risk and its computation. Math Financ Econom. 2013;7(2):229–246.
  • Ararat Ç., Hamel AH, Rudloff B. Set-valued shortfall and divergence risk measures. Int J Theor Appl Finance. 2017;20(5):1750026.
  • Feinstein Z, Rudloff B, Weber S. Measures of systemic risk. SIAM J Financ Math. 2017;8(1):672–708.
  • Ararat Ç., Rudloff B. Dual representations for systemic risk measures. Math Financ Econom. 2020;14(1):139–174.
  • Jouini E, Meddeb M, Touzi N. Vector-valued coherent risk measures. Finance Stoch. 2004;8:531–552.
  • Feinstein Z, Rudloff B. A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle. J Global Optim. 2017;68:47–69.
  • Molchanov I, Cascos I. Multivariate risk measures: a constructive approach based on selections. Math Finance. 2014;26(4):867–900.
  • Hamel A, Heyde F. Duality for set-valued measures of risk. SIAM J Financial Math. 2010;1:66–95.
  • Kulikov AV. Multidimensional coherent and convex risk measures. Theory Probab Appl. 2008;52:614–635.
  • Landsman Z, Makov U, Shushi T. Multivariate tail conditional expectation for elliptical distributions. Insur Math Econom. 2016;70:216–223.
  • Meraklı M, Küçükyavuz S. Vector-valued multivariate conditional value-at-risk. Oper Res Lett. 2018;46:300–305.
  • Noyan N, Rudolf G. Optimization with multivariate conditional value-at-risk constraints. Oper Res. 2013;61:990–1013.
  • Kaina M, Ruschendorf L. On convex risk measures on Lp-spaces. Math Meth Oper Res. 2009;69:475–495.
  • McNeil AJ, Frey R, Embrechts P. The quantitative risk management. Princeton (NJ): Princeton University Press; 2015.
  • Grimmett GR, Stirzaker DR. Probability and random processes. Vol. 80. Oxford: Oxford University Press; 2001.
  • Kotz S, Nadarajah S. Multivariate t distributions and their applications. Cambridge: Cambridge University Press; 2004.
  • Shapiro A. Consistency of sample estimates of risk averse stochastic programs. J Appl Probab. 2013;50:533–541.
  • Guigues V, Kratschmer V, Shapiro A. A central limit theorem and hypotheses testing for risk-averse stochastic programs. SIAM J Optim. 2018;28(2):1337–1366.

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