Inverse Optimization of Convex Risk Functions

References

• Acerbi C (2002) Spectral measures of risk: A coherent representation of subjective risk aversion. J. Bank. Finance 26(7):1505–1518.Crossref, Google Scholar
• Ahuja RK, Orlin JB (2001) Inverse optimization. Oper. Res. 49(5):771–783.Link, Google Scholar
• Armbruster B, Delage E (2015) Decision making under uncertainty when preference information is incomplete. Management Sci. 61(1):111–128.Link, Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Aswani A, Shen Z-JM, Siddiq A (2015) Inverse optimization with noisy data. Oper. Res. 66(3): 597–892.Google Scholar
• Ben-Tal A, den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Ben-Tal A, Teboulle M (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.Crossref, Google Scholar
• Bertsimas D, Gupta V, Paschalidis ICh (2012) Inverse optimization: A new perspective on the blacklitterman model. Oper. Res. 60(6):1389–1403.Link, Google Scholar
• Bertsimas D, Gupta V, Paschalidis IC (2015) Data-driven estimation in equilibrium using inverse optimization. Math. Programming A 153:595–633.Google Scholar
• Birge JR, Hortaçsu A, Pavlin JM (2017) Inverse optimization for the recovery of market structure from market outcomes: an application to the miso electricity market. Oper. Res. 65(4):837–855.Link, Google Scholar
• Boutilier C, Patrascu R, Poupart P, Schuurmans D (2006) Constraint-based optimization and utility elicitation using the minimax decision criterion. Artificial Intelligence 170(8-9):686–713.Crossref, Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, New York).Crossref, Google Scholar
• Burton D, Toint PL (1992) On an instance of the inverse shortest paths problem. Math. Programming 53:45–61.Crossref, Google Scholar
• Chan TC, Craig T, Lee T, Sharpe MB (2014) Generalized inverse multiobjective optimization with application to cancer therapy. Oper. Res. 62:680–695.Link, Google Scholar
• Chan TCY, Lee T, Terekhov D (2019) Inverse optimization: Closed-form solutions, geometry, and goodness of fit. Management Sci. 65(3):1115–1135.Google Scholar
• Clemen RT, Reilly T (2014) Making Hard Decisions with Decisiontools Suite, 3rd ed. (South-Western, Mason, OH).Google Scholar
• Debreu G (1954) Representation of a preference ordering by a numerical function. Thrall RM, Davis RL, Coombs CH, eds. Decision Processes (John Wiley & Sons, New York), 159–165.Google Scholar
• Delage E, Li JY (2018) Minimizing risk exposure when the choice of a risk measure is ambigious. Management Sci. 64(1):327–344.Link, Google Scholar
• DeMiguel V, Garlappi L, Nogales FJ, Uppal R (2009) A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Sci. 55(5):798–812.Link, Google Scholar
• Dempe S, Lohse S (2006) Inverse linear programming. Seeger A, ed. Recent Advances in Optimization (Springer, Berlin), 19–28.Crossref, Google Scholar
• Drapeau S, Kupper M (2013) Risk preferences and their robust representation. Math. Oper. Res. 38(1):28–62.Link, Google Scholar
• Fabozzi FJ (2015) Capital Markets: Institutions, Instruments, and Risk Management, vol 1, 5th ed. (MIT Press, Cambridge, MA).Google Scholar
• Föllmer H, Schied A (2002) Convex measures of risk and trading constraints. Finance Stochastics 6(4):429–447.Crossref, Google Scholar
• Ghate A (2015) Inverse optimization in countably infinite linear programs. Oper. Res. Lett. 43(3):231–235.Crossref, Google Scholar
• Haskell WB, Huang W, Xu H 2018. Preference elicitation and robust optimization with multi-attribute quasi-concave choice functions. Preprint, submitted May 17, 2018, https://arxiv.org/abs/1805.06632.Google Scholar
• Heuberger C (2004) Inverse combinatorial optimization: A survey on problems, methods, and results. J. Combinational Optim. 8:329–361.Crossref, Google Scholar
• Hochbaum DS (2003) Efficient algorithms for the inverse spanning-tree problem. Oper. Res. 51:785–797.Link, Google Scholar
• Hu J, Mehrotra S (2015) Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization. IIE Trans. 47:1–15.Google Scholar
• Iyengar G, Kang W (2005) Inverse conic programming with applications. Oper. Res. Lett. 33(3):319–330.Crossref, Google Scholar
• Keshavarz A, Wang Y, Boyd S (2011) Imputing a convex objective function. IEEE Internat. Sympos. Intelligent Control (Denver, CO), 613–619.Google Scholar
• Kusuoka S (2001) On law invariant coherent risk measures. Kusuoka S, Maruyama T, eds. Advances in Mathematical Economics, vol. 3 (Springer Japan, Tokyo), 83–95.Crossref, Google Scholar
• Lofberg J (2004) Yalmip: A toolbox for modeling and optimization in matlab. IEEE Internat. Sympos. Comput. Aided Control Systems Design (New Orleans), 284–289.Google Scholar
• Mohajerin Esfahani P, Shafieezadeh-Abadeh S, Adiwena Hanasusanto G, Kuhn D (2018) Data-driven inverse optimization with incomplete information. Math. Programming 167(1):191–234.Crossref, Google Scholar
• Natarajan K, Sim M, Uichanco J (2010) Tractable robust expected utility and risk models for portfolio optimization. Math. Finance 20(4):695–731.Crossref, Google Scholar
• Nemirovski A (2006) Advances in convex optimization: Conic programming. Sanz-Sole M, Soria J, Varona JL, Verdera J, eds. Proc. Internat. Congress Mathematicians, vol. I (European Mathematical Society, Madrid), 413–444.Google Scholar
• Rockafellar RT (1974) Conjugate Duality and Optimization. Regional Conference Series in Applied Mathematics (SIAM, Philadelphia).Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2:21–41.Crossref, Google Scholar
• Roy AD (1952) Safety first and the holding of assets. Econometrica 20(3):431–450.Crossref, Google Scholar
• Ruszczyński A, Shapiro A (2006) Optimization of convex risk functions. Math. Oper. Res. 31(3):433–452.Link, Google Scholar
• Savage LJ (1954) The Foundations of Statistics (Wiley, New York).Google Scholar
• Schaefer AJ (2009) Inverse integer programming. Optim. Lett. 3:483–489.Crossref, Google Scholar
• Von Neumann J, Morgenstern O (1944) Theory of Games and Economic Behavior (Princeton Univ. Press, Princeton).Google Scholar
• Zhang J, Liu Z (1996) Calculating some inverse linear programming problems. J. Comput. Appl. Math. 72(2):261–273.Crossref, Google Scholar
• Zhang J, Xu C (2010) Inverse optimization for linearly constrained convex separable programming problems. Eur. J. Oper. Res. 200:671–679.Crossref, Google Scholar