Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach

[EN] Sustainable finance, which integrates environmental, social and governance criteria on financial decisions rests on the fact that money should be used for good purposes. Thus, the financial sector is also expected to play a more important role to decarbonise the global economy. To align financial flows with a pathway towards a low-carbon economy, investors should be able to integrate into their financial decisions additional criteria beyond return and risk to manage climate risk. We propose a tri-criterion portfolio selection model to extend the classical Markowitz's mean-variance approach to include investor's preferences on the portfolio carbon risk exposure as an additional criterion. To approximate the 3D Pareto front we apply an efficient multi-objective genetic algorithm called ev-MOGA which is based on the concept of epsilon-dominance. Furthermore, we introduce a-posteriori approach to incorporate the investor's preferences into the solution process regarding their climate-change related preferences measured by the carbon risk exposure and their loss-adverse attitude. We test the performance of the proposed algorithm in a cross-section of European socially responsible investments open-end funds to assess the extent to which climate-related risk could be embedded in the portfolio according to the investor's preferences.Hilario Caballero, A.; Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Vercher, M. (2020). Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach. International Journal of Environmental research and Public Health. 17(17):1-15. https://doi.org/10.3390/ijerph17176324S1151717Morningstar Low Carbon Designationhttps://bit.ly/2SfAFUAKrueger, P., Sautner, Z., & Starks, L. T. (2020). The Importance of Climate Risks for Institutional Investors. The Review of Financial Studies, 33(3), 1067-1111. doi:10.1093/rfs/hhz137Syam, S. S. (1998). A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals. European Journal of Operational Research, 108(1), 196-207. doi:10.1016/s0377-2217(97)00048-9Li, D., Sun, X., & Wang, J. (2006). OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN-VARIANCE FORMULATION FOR PORTFOLIO SELECTION. Mathematical Finance, 16(1), 83-101. doi:10.1111/j.1467-9965.2006.00262.xBertsimas, D., & Shioda, R. (2007). Algorithm for cardinality-constrained quadratic optimization. Computational Optimization and Applications, 43(1), 1-22. doi:10.1007/s10589-007-9126-9Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121. doi:10.1016/0304-405x(75)90025-2Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Mansini, R. (2003). LP solvable models for portfolio optimization: a classification and computational comparison. IMA Journal of Management Mathematics, 14(3), 187-220. doi:10.1093/imaman/14.3.187Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302. doi:10.1016/s0305-0548(99)00074-xMaringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25(4), 481-495. doi:10.1007/s00291-003-0139-1Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23(3), 411-420. doi:10.1080/10556780701722542Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063. doi:10.1016/j.eswa.2008.06.007Anagnostopoulos, K. P., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications. doi:10.1016/j.eswa.2011.04.233Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37, 104-125. doi:10.1016/j.swevo.2017.06.005Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 267(1-2), 281-319. doi:10.1007/s10479-016-2377-zMetaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Liagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Babaei, S., Sepehri, M. M., & Babaei, E. (2015). Multi-objective portfolio optimization considering the dependence structure of asset returns. European Journal of Operational Research, 244(2), 525-539. doi:10.1016/j.ejor.2015.01.025Ruiz, A. B., Saborido, R., Bermúdez, J. D., Luque, M., & Vercher, E. (2019). Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences. Journal of Global Optimization, 76(2), 295-315. doi:10.1007/s10898-019-00782-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hu, Y., Chen, H., He, M., Sun, L., Liu, R., & Shen, H. (2019). Multi-Swarm Multi-Objective Optimizer Based on p-Optimality Criteria for Multi-Objective Portfolio Management. Mathematical Problems in Engineering, 2019, 1-22. doi:10.1155/2019/8418369Rangel-González, J. A., Fraire, H., Solís, J. F., Cruz-Reyes, L., Gomez-Santillan, C., Rangel-Valdez, N., & Carpio-Valadez, J. M. (2020). Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem. International Journal of Fuzzy Systems, 22(8), 2760-2768. doi:10.1007/s40815-020-00928-4Garcia-Bernabeu, A., Salcedo, J. V., Hilario, A., Pla-Santamaria, D., & Herrero, J. M. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity, 2019, 1-12. doi:10.1155/2019/6095712Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Matlab Central: ev-MOGA Multiobjective Evolutionary Algorithmhttps://bit.ly/3f2BYQMBlasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

[EN] The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio's performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). Sectoral integration and investment diversification opportunities: evidence from Colombo Stock Exchange. Entrepreneurship and Sustainability Issues, 5(3), 514-527. doi:10.9770/jesi.2018.5.3(8)Arenas Parra, M., Bilbao Terol, A., & Rodrı́guez Urı́a, M. V. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133(2), 287-297. doi:10.1016/s0377-2217(00)00298-8Arribas, I., Espinós-Vañó, M. D., García, F., & Tamošiūnienė, R. (2019). Negative screening and sustainable portfolio diversification. Entrepreneurship and Sustainability Issues, 6(4), 1566-1586. doi:10.9770/jesi.2019.6.4(2)Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203-228. doi:10.1111/1467-9965.00068Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121. doi:10.1016/0304-405x(75)90025-2Bermúdez, J. D., Segura, J. V., & Vercher, E. (2012). A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188(1), 16-26. doi:10.1016/j.fss.2011.05.013Bezoui, M., Moulaï, M., Bounceur, A., & Euler, R. (2018). An iterative method for solving a bi-objective constrained portfolio optimization problem. Computational Optimization and Applications, 72(2), 479-498. doi:10.1007/s10589-018-0052-9Bi, T., Zhang, B., & Wu, H. (2013). Measuring Downside Risk Using High-Frequency Data: Realized Downside Risk Measure. Communications in Statistics - Simulation and Computation, 42(4), 741-754. doi:10.1080/03610918.2012.655826Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems, 131(1), 13-21. doi:10.1016/s0165-0114(01)00251-2Chen, W., & Xu, W. (2018). A Hybrid Multiobjective Bat Algorithm for Fuzzy Portfolio Optimization with Real-World Constraints. International Journal of Fuzzy Systems, 21(1), 291-307. doi:10.1007/s40815-018-0533-0Choobineh, F., & Branting, D. (1986). A simple approximation for semivariance. European Journal of Operational Research, 27(3), 364-370. doi:10.1016/0377-2217(86)90332-2Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Fang, Y., Lai, K. K., & Wang, S.-Y. (2006). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 175(2), 879-893. doi:10.1016/j.ejor.2005.05.020Favre, L., & Galeano, J.-A. (2002). Mean-Modified Value-at-Risk Optimization with Hedge Funds. The Journal of Alternative Investments, 5(2), 21-25. doi:10.3905/jai.2002.319052García, F., González-Bueno, J., Guijarro, F., & Oliver, J. (2020). Forecasting the Environmental, Social, and Governance Rating of Firms by Using Corporate Financial Performance Variables: A Rough Set Approach. Sustainability, 12(8), 3324. doi:10.3390/su12083324García, González-Bueno, Oliver, & Riley. (2019). Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability, 11(9), 2496. doi:10.3390/su11092496García, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA. Journal of Business Economics and Management, 20(2), 225-243. doi:10.3846/jbem.2019.8317García, F., Guijarro, F., & Moya, I. (2013). A MULTIOBJECTIVE MODEL FOR PASSIVE PORTFOLIO MANAGEMENT: AN APPLICATION ON THE S&P 100 INDEX. Journal of Business Economics and Management, 14(4), 758-775. doi:10.3846/16111699.2012.668859García, F., Guijarro, F., & Oliver, J. (2017). Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Computing and Applications, 30(8), 2625-2641. doi:10.1007/s00521-017-2882-2García, F., Guijarro, F., Oliver, J., & Tamošiūnienė, R. (2018). HYBRID FUZZY NEURAL NETWORK TO PREDICT PRICE DIRECTION IN THE GERMAN DAX-30 INDEX. Technological and Economic Development of Economy, 24(6), 2161-2178. doi:10.3846/tede.2018.6394Goel, A., Sharma, A., & Mehra, A. (2018). Index tracking and enhanced indexing using mixed conditional value-at-risk. Journal of Computational and Applied Mathematics, 335, 361-380. doi:10.1016/j.cam.2017.12.015González-Bueno, J. (2019). Optimización multiobjetivo para la selección de carteras a la luz de la teoría de la credibilidad. Una aplicación en el mercado integrado latinoamericano. Editorial Universidad Pontificia Bolivariana.Gupta, P., Inuiguchi, M., & Mehlawat, M. K. (2011). A hybrid approach for constructing suitable and optimal portfolios. Expert Systems with Applications, 38(5), 5620-5632. doi:10.1016/j.eswa.2010.10.073Gupta, P., Inuiguchi, M., Mehlawat, M. K., & Mittal, G. (2013). Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints. Information Sciences, 229, 1-17. doi:10.1016/j.ins.2012.12.011Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization Using Credibility Theory. Studies in Fuzziness and Soft Computing, 127-160. doi:10.1007/978-3-642-54652-5_5Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization with Interval Coefficients. Studies in Fuzziness and Soft Computing, 33-59. doi:10.1007/978-3-642-54652-5_2Gupta, P., Mehlawat, M. K., Kumar, A., Yadav, S., & Aggarwal, A. (2020). A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns. International Journal of Fuzzy Systems, 22(3), 824-843. doi:10.1007/s40815-020-00801-4Gupta, P., Mehlawat, M. K., & Saxena, A. (2010). A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality. Information Sciences, 180(11), 2264-2285. doi:10.1016/j.ins.2010.02.007Gupta, P., Mehlawat, M. K., Yadav, S., & Kumar, A. (2020). Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft Computing, 24(16), 11931-11956. doi:10.1007/s00500-019-04639-3Gupta, P., Mittal, G., & Mehlawat, M. K. (2013). Expected value multiobjective portfolio rebalancing model with fuzzy parameters. Insurance: Mathematics and Economics, 52(2), 190-203. doi:10.1016/j.insmatheco.2012.12.002Heidari-Fathian, H., & Davari-Ardakani, H. (2019). Bi-objective optimization of a project selection and adjustment problem under risk controls. Journal of Modelling in Management, 15(1), 89-111. doi:10.1108/jm2-07-2018-0106Hilkevics, S., & Semakina, V. (2019). The classification and comparison of business ratios analysis methods. Insights into Regional Development, 1(1), 48-57. doi:10.9770/ird.2019.1.1(4)Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177(2), 500-507. doi:10.1016/j.amc.2005.11.027Huang, X. (2008). Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics, 217(1), 1-8. doi:10.1016/j.cam.2007.06.009Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263-281. doi:10.1007/s10700-009-9064-3Huang, X. (2010). Portfolio Analysis. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-642-11214-0Huang, X. (2017). A review of uncertain portfolio selection. Journal of Intelligent & Fuzzy Systems, 32(6), 4453-4465. doi:10.3233/jifs-169211Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284-296. doi:10.1016/j.amc.2015.12.018Huang, X., & Wang, X. (2019). International portfolio optimization based on uncertainty theory. Optimization, 70(2), 225-249. doi:10.1080/02331934.2019.1705821Huang, X., & Yang, T. (2020). How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk. Journal of Banking & Finance, 111, 105726. doi:10.1016/j.jbankfin.2019.105726Jalota, H., Thakur, M., & Mittal, G. (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40-56. doi:10.1016/j.eswa.2016.11.014Jalota, H., Thakur, M., & Mittal, G. (2017). A credibilistic decision support system for portfolio optimization. Applied Soft Computing, 59, 512-528. doi:10.1016/j.asoc.2017.05.054Kaplan, P. D., & Alldredge, R. H. (1997). Semivariance in Risk-Based Index Construction. The Journal of Investing, 6(2), 82-87. doi:10.3905/joi.1997.408419Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Li, B., Zhu, Y., Sun, Y., Aw, G., & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539-550. doi:10.1016/j.apm.2017.12.016Li, H.-Q., & Yi, Z.-H. (2019). Portfolio selection with coherent Investor’s expectations under uncertainty. Expert Systems with Applications, 133, 49-58. doi:10.1016/j.eswa.2019.05.008Li, X., & Qin, Z. (2014). Interval portfolio selection models within the framework of uncertainty theory. Economic Modelling, 41, 338-344. doi:10.1016/j.econmod.2014.05.036Liagkouras, K., & Metaxiotis, K. (2015). Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics. International Journal of Information Technology & Decision Making, 14(03), 535-564. doi:10.1142/s0219622015300013Liu, B. (2004). Uncertainty Theory. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-39987-2Baoding Liu, & Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. doi:10.1109/tfuzz.2002.800692Liu, N., Chen, Y., & Liu, Y. (2018). Optimizing portfolio selection problems under credibilistic CVaR criterion. Journal of Intelligent & Fuzzy Systems, 34(1), 335-347. doi:10.3233/jifs-171298Liu, Y.-J., & Zhang, W.-G. (2018). Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory. International Journal of Information Technology & Decision Making, 17(03), 941-968. doi:10.1142/s0219622018500190Mansour, N., Cherif, M. S., & Abdelfattah, W. (2019). Multi-objective imprecise programming for financial portfolio selection with fuzzy returns. Expert Systems with Applications, 138, 112810. doi:10.1016/j.eswa.2019.07.027Markowitz, H. (1952). PORTFOLIO SELECTION*. The Journal of Finance, 7(1), 77-91. doi:10.1111/j.1540-6261.1952.tb01525.xMarkowitz, H., Todd, P., Xu, G., & Yamane, Y. (1993). Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307-317. doi:10.1007/bf02282055Martin, R. D., Rachev, S. (Zari), & Siboulet, F. (2003). Phi-alpha optimal portfolios and extreme risk management. Wilmott, 2003(6), 70-83. doi:10.1002/wilm.42820030619Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information Sciences, 345, 9-26. doi:10.1016/j.ins.2016.01.042Mehlawat, M. K., Gupta, P., Kumar, A., Yadav, S., & Aggarwal, A. (2020). Multiobjective Fuzzy Portfolio Performance Evaluation Using Data Envelopment Analysis Under Credibilistic Framework. IEEE Transactions on Fuzzy Systems, 28(11), 2726-2737. doi:10.1109/tfuzz.2020.2969406Mehralizade, R., Amini, M., Sadeghpour Gildeh, B., & Ahmadzade, H. (2020). Uncertain random portfolio selection based on risk curve. Soft Computing, 24(17), 13331-13345. doi:10.1007/s00500-020-04751-9Moeini, M. (2019). Solving the index tracking problem: a continuous optimization approach. Central European Journal of Operations Research. doi:10.1007/s10100-019-00633-0Narkunienė, J., & Ulbinaitė, A. (2018). Comparative analysis of company performance evaluation methods. Entrepreneurship and Sustainability Issues, 6(1), 125-138. doi:10.9770/jesi.2018.6.1(10)Palanikumar, K., Latha, B., Senthilkumar, V. S., & Karthikeyan, R. (2009). Multiple performance optimization in machining of GFRP composites by a PCD tool using non-dominated sorting genetic algorithm (NSGA-II). Metals and Materials International, 15(2), 249-258. doi:10.1007/s12540-009-0249-7Pflug, G. C. (2000). Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk. Probabilistic Constrained Optimization, 272-281. doi:10.1007/978-1-4757-3150-7_15Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2(3), 21-41. doi:10.21314/jor.2000.038Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Rubio, A., Bermúdez, J. D., & Vercher, E. (2016). Forecasting portfolio returns using weighted fuzzy time series methods. International Journal of Approximate Reasoning, 75, 1-12. doi:10.1016/j.ijar.2016.03.007Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63. doi:10.1016/j.asoc.2015.11.005Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(S1), 119. doi:10.1086/294846Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/jpm.1994.409501Sortino, F. A., & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. The Journal of Investing, 3(3), 59-64. doi:10.3905/joi.3.3.59Srinivas, N., & Deb, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3), 221-248. doi:10.1162/evco.1994.2.3.221Vercher, E., & Bermúdez, J. D. (2012). Fuzzy Portfolio Selection Models: A Numerical Study. Financial Decision Making Using Computational Intelligence, 253-280. doi:10.1007/978-1-4614-3773-4_10Vercher, E., & Bermudez, J. D. (2013). A Possibilistic Mean-Downside Risk-Skewness Model for Efficient Portfolio Selection. IEEE Transactions on Fuzzy Systems, 21(3), 585-595. doi:10.1109/tfuzz.2012.2227487Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131. doi:10.1016/j.eswa.2015.05.020Vercher, E., Bermúdez, J. D., & Segura, J. V. (2007). Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems, 158(7), 769-782. doi:10.1016/j.fss.2006.10.026Wang, S., & Zhu, S. (2002). Fuzzy Optimization and Decision Making, 1(4), 361-377. doi:10.1023/a:1020907229361Yue, W., & Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465, 124-140. doi:10.1016/j.physa.2016.08.009Yue, W., Wang, Y., & Xuan, H. (2018). Fuzzy multi-objective portfolio model based on semi-variance–semi-absolute deviation risk measures. Soft Computing, 23(17), 8159-8179. doi:10.1007/s00500-018-3452-yZadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xZhai, J., & Bai, M. (2018). Mean-risk model for uncertain portfolio selection with background risk. Journal of Computational and Applied Mathematics, 330, 59-69. doi:10.1016/j.cam.2017.07.038Zhao, Z., Wang, H., Yang, X., & Xu, F. (2020). CVaR-cardinality enhanced indexation optimization with tunable short-selling constraints. Applied Economics Letters, 28(3), 201-207. doi:10.1080/13504851.2020.174015

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

Moments and Semi-Moments for fuzzy portfolios selection

The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.Fuzzy moments, Credibility theory, Portfolios, Asset allocation, multi-objective optimization