Portfolio reshaping under 1st-order stochastic dominance constraints by the exact penalty function methods

References

• Norkin VI. The projective exact penalty method for general constrained optimization. Preprint. V. M. Glushkov Institute of Cybernetics, Kyiv, 2022..
   Google Scholar
• Dentcheva D, Ruszczyński A. Optimization with stochastic dominance constraints. SIAM J Optim. 2003;14:548–566. doi: 10.1137/s1052623402420528
   Web of Science ®Google Scholar
• Dentcheva D, Ruszczyński A. Portfolio optimization with stochastic dominance constraints. J Bank Financ. 2006;30:433–451. doi: 10.1016/j.jbankfin.2005.04.024
   Web of Science ®Google Scholar
• Noyan N, Rudolf G, Ruszczyński A. Relaxations of linear programming problems with first order stochastic dominance constraints. Oper Res Lett. 2006;34:653–659. doi: 10.1016/j.orl.2005.10.004
   Web of Science ®Google Scholar
• Noyan N, Ruszczyński A. Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints. Math Program. 2008;114:249–275. doi: 10.1007/s10107-007-0100-1
   Web of Science ®Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A. Lectures on stochastic programming. 3rd ed. SIAM; 2021. (MOS-SIAM Series on Optimization). doi: 10.1137/1.9781611976595
   Google Scholar
• Gutjahr WJ, Pichler A. Stochastic multi-objective optimization: a survey on non-scalarizing methods. Ann Oper Res. 2013;236(2):1–25. doi: 10.1007/s10479-013-1369-5
   Google Scholar
• Markowitz HM. Portfolio selection. J Finance. 1952;7(1):77–91. doi: 10.2307/2975974
   Web of Science ®Google Scholar
• Roy AD. Safety first and the holding of assets. Econometrica. 1952;20:431–449. doi: 10.2307/1907413
   Web of Science ®Google Scholar
• Artzner P, Delbaen F, Eber J-M, et al. Coherent measures of risk. Math Financ. 1999;9:203–228. doi: 10.1111/mafi.1999.9.issue-3
   Web of Science ®Google Scholar
• Benati S, Rizzi R. A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem. Eur J Oper Res. 2007;176:423–434. doi: 10.1016/j.ejor.2005.07.020
   Web of Science ®Google Scholar
• Gaivoronski AA, Pflug GC. Finding optimal portfolios with constraints on value-at-rrisk. In: Green B, editor, Proceedings of the Third International Stockholm Seminar on Risk Behaviour and Risk Management. Stockholm University; 1999.
   Google Scholar
• Gaivoronski AA, Pflug GC. Value at risk in portfolio optimization: properties and computational approach. J Risk. 2005;7:1–31. doi: 10.21314/JOR.2005.106
   Google Scholar
• Kataoka S. A stochastic programming model. Econometrica. 1963;31:181–196. doi: 10.2307/1910956
   Web of Science ®Google Scholar
• Kibzun AI, Kan YS. Stochastic programming problems with probability and quantile functions. Chichester: John Wiley & Sons; 1996.
   Google Scholar
• Kibzun AI, Naumov AV, Norkin VI. On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem. Autom Remote Control. 2013;74:951–967. doi: 10.1134/S0005117913060064
   Web of Science ®Google Scholar
• Kirilyuk V. Risk measures in stochastic programming and robust optimization problems. Cybern Syst Anal. 2015;51:874–885. doi: 10.1007/s10559-015-9780-3
   Google Scholar
• Luedtke J, Ahmed S, Nemhauser G. An integer programming approach for linear programs with probabilistic constraints. Math Program. 2010;122:247–272. doi: 10.1007/s10107-008-0247-4
   Web of Science ®Google Scholar
• Norkin VI, Boyko SV. Safety-first portfolio selection. Cybern Syst Anal. 2012;48:180–191. doi: 10.1007/s10559-012-9396-9
   Google Scholar
• Norkin VI, Kibzun AI, Naumov AV. Reducing two-stage probabilistic optimization problems with discrete distribution of random data to mixed-integer programming problems. Cybern Syst Anal. 2014;50:679–692. doi: 10.1007/s10559-014-9658-9
   Google Scholar
• Pflug GC, Römisch W. Modeling, measuring and managing risk. River Edge (NJ): World Scientific; 2007. doi: 10.1142/9789812708724
   Google Scholar
• Prekopa A. Stochastic programming. Dordreht: Kluwer Academic Publisher; 1995.
   Google Scholar
• Sen S. Relaxation for probabilistically constrained programs with discrete random variables. Oper Res Lett. 1992;11:81–86. doi: 10.1016/0167-6377(92)90037-4
   Web of Science ®Google Scholar
• Telser LG. Safety first and hedging. Rev Econ Stud. 1955/56;23:1–16. doi: 10.2307/2296146
   Web of Science ®Google Scholar
• Wozabal D, Hochreiter R, Pflug GC. A D. C. formulation of value-at-risk constrained optimization. Optimization. 2010;59:377–400. doi: 10.1080/02331931003700731
   Web of Science ®Google Scholar
• Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. J Risk. 2000;2(3):21–41. doi: 10.21314/JOR.2000.038
   Google Scholar
• Dentcheva D, Ruszczyński A. Risk preferences on the space of quantile functions. Math Program Ser B. 2013;148:181–200. doi: 10.1007/s10107-013-0724-2
   Web of Science ®Google Scholar
• Müller A, Stoyan D. Comparison methods for stochastic models and risks. Chichester: John Wiley & Sons; 2002.
   Google Scholar
• Ogryczak W, Ruszczyński A. From stochastic dominance to mean-risk models: semideviations as risk measures. Eur J Oper Res. 1999;116:33–50. doi: 10.1016/S0377-2217(98)00167-2
   Web of Science ®Google Scholar
• Ogryczak W, Ruszczyński A. On consistency of stochastic dominance and mean–semideviation models. Math Program Ser B. 2001;89:217–232. doi: 10.1007/s101070000203
   Web of Science ®Google Scholar
• Ogryczak W, Ruszczyński A. Dual stochastic dominance and related mean-risk models. SIAM J Optim. 2002;13(1):60–78. doi: 10.1137/S1052623400375075
   Web of Science ®Google Scholar
• Dentcheva D, Ruszczyński A. Common mathematical foundations of expected utility and dual utility theories. SIAM J Optim. 2013;23(1):381–405. doi: 10.1137/120868311
   Web of Science ®Google Scholar
• Dai H, Xue Y, He N, et al. Learning to optimize with stochastic dominance constraints. In: International Conference on Artificial Intelligence and Statistics, PMLR; 2023; p. 8991–9009.
   Google Scholar
• Dentcheva D, Ruszczyński A. Portfolio optimization with risk control by stochastic dominance constraints. In: Infanger G., editor, Stochastic Programming. The State of the Art. In Honor of George B. Dantzig, chapter 9, pages 189–212. New York: Springer; 2011.
   Google Scholar
• Fábián CI, Mitra G, Roman D, et al. Portfolio choice models based on second-order stochastic dominance measures: An overview and a computational study. In M. Bertocchi, G. Consigli, and M. A. H. Dempster, editors, Stochastic optimization methods in finance and energy, International Series in Operations Research & Management Science, chapter 18, Springer: New York; 2011; p. 441–470. ISBN 978-1-4419-9586-5. doi: 10.1007/978-1-4419-9586-5_18
   Google Scholar
• Dentcheva D, Ruszczyński A. Risk preferences on the space of quantile functions. Math Program. 2014;148(1-2):181–200. doi: 10.1007/s10107-013-0724-2
   Web of Science ®Google Scholar
• Dentcheva D, Ruszczyński A. Semi-infinite probabilistic optimization: first order stochastic dominance constraints. Optimization. 2004;53:583–601. doi: 10.1080/02331930412331327148
   Web of Science ®Google Scholar
• Dentcheva D, Henrion R, Ruszczyński A. Stability and sensitivity of optimization problems with first order stochastic dominance constraints. SIAM J Optim. 2007;18:322–337. doi: 10.1137/060650118
   Web of Science ®Google Scholar
• Frydenberg S, Sønsteng Henriksen TE, Pichler A, et al. Can commodities dominate stock and bond portfolios? Ann Oper Res. 2019;282(1-2):155–177. doi: 10.1007/s10479-018-2996-7
   Web of Science ®Google Scholar
• Batukhtin V. On solving discontinuous extremal problems. J Optim Theory Appl. 1993;77:575–589. doi: 10.1007/BF00940451
   Web of Science ®Google Scholar
• Knopov P, Norkin V. Stochastic optimization methods for the stochastic storage process control. M. J. Blondin et al. (eds.), Intelligent Control and Smart Energy Management, Springer Optimization and Its Applications 181, 2022; p. 79–111. doi: 10.1007/978-3-030-84474-5_3
   Google Scholar
• Norkin VI. A stochastic smoothing method for nonsmooth global optimization. Cybernetics and Computer technologies: 2020; p. 5–14. doi: 10.34229/2707-451X.20.1.1
   Google Scholar
• Ermoliev YM, Norkin VI, Wets RJ-B. The minimization of semicontinuous functions: mollifier subgradients. SIAM J Control Optim. 1995;33:149–167. doi: 10.1137/S0363012992238369
   Web of Science ®Google Scholar
• Mayne D, Polak E. On solving discontinuous extremal problems. J Optim Theory Appl. 1984;43:601–613. doi: 10.1007/BF00935008
   Google Scholar
• Mikhalevich VS, Gupal AM, Norkin VI. Methods of nonconvex optimization. Moscow: Nauka; 1987. (In Russian).
   Google Scholar
• Nesterov Y, Spokoiny V. Random gradient-free minimization of convex functions. Found Comput Math. 2017;17:527–566. doi: 10.1007/s10208-015-9296-2
   Web of Science ®Google Scholar
• Norkin V, Pflug GC, Ruszczyński A. A branch and bound method for stochastic global optimization. Math Program. 1998;83:425–450. doi: 10.1007/bf02680569
   Web of Science ®Google Scholar
• Aubin J-P, Ekeland I. Applied nonlinear analysis. New York: John Wiley and Sons; 1984.
   Google Scholar
• Norkin VI. On measuring and profiling catastrophic risks. Cybern Syst Anal. 2006;42(6):839–850. doi: 10.1007/s10559-006-0124-1
   Google Scholar
• Galvan G, Sciandrone M, Eucidi S. A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints. Comput Optim Appl. 2021;80:33–53. doi: 10.1007/s10589-021-00296-1
   Web of Science ®Google Scholar
• Rockafellar RT, Wets RJ-B. Variational analysis. Grundlehren der mathematischen Wissenschaften. Springer, 1st ed. 1998, 3rd printing, springer edition, 2009. ISBN 3540627723; 9783540627722. doi: 10.1007/978-3-642-02431-3
   Google Scholar
• Ermoliev Y, Norkin V. On constrained discontinuous optimization. In: Stochastic Programming Methods and Technical Applications: Proceedings of the 3rd GAMM/IFIP-Workshop on ‘Stochastic Optimization: Numerical Methods and Technical Applications’ held at the Federal Armed Forces University Munich, Neubiberg/München, Germany, June 17–20, 1996, Springer: Berlin, Heidelberg; 1998; p. 128–144.
   Google Scholar
• Gupal AM, Norkin VI. Algorithm for the minimization of discontinuous functions. Cybernetics. 1977;13(2):220–223. doi: 10.1007/BF01073313
   Google Scholar
• Rockafellar RT, Wets RJ-B. Variational analysis. Switzerland AG: Springer Nature; 1997. Available at https://books.google.com/books?id=w-NdOE5fD8AC.doi: 10.1007/978-3-642-02431-3
   Google Scholar
• Norkin V, Pichler A, Kozyriev A. Constrained global optimization by smoothing. arXiv; 2023. doi: 10.48550/arXiv.2308.08422
   Google Scholar
• Nemirovsky A, Yudin D. Informational complexity and efficient methods for solution of convex extremal problems. New York: J. Wiley & Sons; 1983.
   Google Scholar
• Nesterov Y. A method of solving a convex programming problem with convergence rate. Soviet Math Dokl. 1983;27(2):372–376.
   Google Scholar
• Ermoliev YM. Methods of stochastic programming. Moscow: Nauka; 1976. (In Russian).
   Google Scholar
• Gupal AM. Stochastic methods for minimzation of nondifferentiable functions. Autom Remote Control. 1979;4(40):529–534.
   Google Scholar
• Polyak BT. Introduction to optimization. New York: Optimization Software, Inc. Publications Division; 1987.
   Google Scholar
• Pflug GC. Stepsize rules, stopping times, and their implementation in stochastic quasigradient algorithms. In: Ermoliev Y. and Wets RJ-B, editors, Numerical Techniques for Stochastic Optimization. Berlin: Springer-Verlag; 1988; chapter 17, p. 353–372.
   Google Scholar
• Markowitz HM. Portfolio selection. efficient diversification of investments. New York: John Wiley & Sons, Chapman & Hall; 1959.
   Google Scholar
• Luedtke J. New formulations for optimization under stochastic dominance constraints. SIAM J Optim. 2008;19(3):1433–1450. doi: 10.1137/070707956
   Web of Science ®Google Scholar