Abstract
For index-based hedging design, the scatter plot of the hedging contract losses versus the to-be-hedged losses is generally used to visualize and quantify basis risk. While studying this scatter plot, which does not cluster along the diagonal as desired, a “bundled loss” phenomenon is found. In a setting where both the hedging and the hedged contracts have 100,000 years of simulated losses, this shows that if we need to hedge one loss in a year for the hedged contract, we may need to pay for other losses in other years in the hedging contract, which are unnecessary and unwanted. The reason is that the index used in the hedging may have identical loss values in different years while the hedged contract may not. This finding is a guiding principle for forming the risk measures and solution frameworks. To solve the problem so formed, a hybrid multi-parent and orthogonal crossover genetic algorithm, GA-MPC-OX, is used and pertinent adjustments are studied. For a problem with hundreds of dimensions, using eleven parents seems best, while a problem with tens of dimensions would prefer nine parents. Depending on the dimensions, relevant best strategies of the orthogonal crossover are also suggested by experimental results. To combat the stagnation of the algorithm, the perturbation by Lévy stable distribution is studied. This reveals possible effective parameters and forms. Numerical comparison with other algorithms is also conducted that confirms its competence for the hedging problem.
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References
Wang, F.X.: Relay Optimization Method (May 2014). http://www.optimization-online.org/DB_FILE/2014/05/4345.pdf
Wang, Y., Cai, Z., Zhang, Q.: Enhancing the search ability of differential evolution through orthogonal crossover. Information Sciences 185(1), 153–177 (2012)
Chuang, L.Y., Tsai, S.W., Yang, C.H.: Chaotic catfish particle swarm optimization for solving global numerical optimization problems. Applied Mathematics and Computation 217, 6900–6916 (2011)
Elsayed, S.M., Sarker, R.A., Essam, D.L.: GA with a new multi-parent crossover for solving IEEE-CEC 2011 competition problems. In: Proc. IEEE Congr. Evol. Comput. (CEC), pp. 1034–1040 (2011)
Bayraktar, Z., Komurcu, M., Bossard, J.A., Werner, D.H.: The Wind Driven Optimization Technique and its Application in Electromagnetics. IEEE Transactions on Antennas and Propagation 61(5), 2745–2757 (2013). http://wdo.cloudturkiye.com/wdo_matlab_03.m
Yang, X.S.: Nature-Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press (2010). http://www.mathworks.com/matlabcentral/fileexchange/authors/119376
Weron, R.: STABLERND: MATLAB function to generate random numbers from the stable distribution (April 26, 2010). http://ideas.repec.org/c/boc/bocode/m429003.html
McCulloch, J.H.: Stable Random Number Generator (December 18, 1996). http://www.econ.ohio-state.edu/jhm/programs/STABRND.M
Veillette, M.: STBL: Alpha stable distributions for MATLAB (July 16, 2012). http://www.mathworks.com/matlabcentral/fileexchange/37514-stbl–alpha-stable-distributions-for-matlab
Vaz, A.I.F., Vicente, L.N.: A particle swarm pattern search method for bound constrained global optimization. Journal of Global Optimization 39, 197–219 (2007). http://www.norg.uminho.pt/aivaz/pswarm/
Zhang, Q., Li, H.: MOEA/D: A Multi-objective Evolutionary Algorithm Based on Decomposition. IEEE Trans. on Evolutionary Computation 11(6), 712–731(2007)
Zhang, Q., Liu, W., Li, H.: The Performance of a New Version of MOEA/D on CEC 2009 Unconstrained MOP Test Instances. Working Report CES-491, School of CS & EE. University of Essex (February 2009)
Zhao, S.Z., Suganthan, P.N., Zhang, Q.: MOEA/D with an Ensemble of Neighbourhood Sizes. IEEE Trans. on Evolutionary Computation (TEC) 16(3), 442–446 (2012)
Wang, Y., Cai, Z.: A dynamic hybrid framework for constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 42(1), 203–217 (2012)
Wang, Y., Cai, Z.: Combining multiobjective optimization with differential evolution to solve constrained optimization problems. IEEE Transactions on Evolutionary Computation 16(1), 117–134 (2012)
Jia, G., Wang, Y., Cai, Z., Jin, Y.: An improved (μ+λ)-constrained differential evolution for constrained optimization. Information Sciences 222, 302–322 (2013)
Liu, H., Cai, Z., Wang, Y.: Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Applied Soft Computing 10(2), 629–640 (2010)
Civicioglu, P.: Transforming Geocentric Cartesian Coordinates to Geodetic Coordinates by Using Differential Search Algorithm. Computers and Geosciences 46, 229–247 (2012). http://www.pinarcivicioglu.com/ds.html
Yang, Z., Tang, K., Yao, X.: Large Scale Evolutionary Optimization Using Cooperative Coevolution. Information Sciences 178(15), 2985–2999 (2008)
Yang, Z., Tang, K., Yao, X.: Self-adaptive differential evolution with neighborhood search. In: Proceedings of the 2008 IEEE Congress on Evolutionary Computation (CEC 2008), Hongkong, China (2008)
Wang, Y., Cai, Z., Zhang, Q.: Differential evolution with composite trial vector generation strategies and control parameters. IEEE Transactions on Evolutionary Computation 15(1), 55–66 (2011)
Rao, R.V., Patel, V.: An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems. International Journal of Industrial Engineering Computations 3(4), 535–560(2012). https://sites.google.com/site/tlborao/
Wang, Y., Cai, Z., Zhang, Q.: Enhancing the search ability of differential evolution through orthogonal crossover. Information Sciences 185(1), 153–177 (2012)
Sadollah, A., Bahreininejad, A., Eskandar, H., Hamdi, M.: Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems. Applied Soft Computing 13(5), 2592–2612 (2013)
Wang, Y., Xiang, J., Cai, Z.: A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator. Applied Soft Computing 12(11), 3526–3538 (2012)
Zhou, A., Zhang, Q., Jin, Y.: Approximating the Set of Pareto Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm. IEEE Trans. on Evolutionary Computation 13(5), 1167–1189 (2009)
Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: A Regularity Model Based Multiobjective Estimation of Distribution Algorithm. IEEE Trans. on Evolutionary Computation 12(1), 41–63 (2008)
Karaboga, D., Basturk, B.: A powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm. Journal of Global Optimization 39(3), 459–171 (2007). http://www.mathworks.com/matlabcentral/fileexchange/27125-solution-to-economic-dispatch-by-artificial-bee-colony-algorithm/content/ABC-eld/runABC.m
Tsai, P.W., Pan, J.S., Liao, B.Y., Chu, S.C.: Enhanced artificial bee colony optimization. International Journal of Innovative Computing, Information and Control 5(12), 5081–5092 (2009)
Special Session & Competition on Real-Parameter Single Objective Optimization at CEC 2013, June 21-23, Cancun, Mexico (2013). http://www.ntu.edu.sg/home/EPNSugan/index_files/CEC2013/CEC2013.htm
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Wang, F.X. (2015). Design Index-Based Hedging: Bundled Loss Property and Hybrid Genetic Algorithm. In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds) Advances in Swarm and Computational Intelligence. ICSI 2015. Lecture Notes in Computer Science(), vol 9140. Springer, Cham. https://doi.org/10.1007/978-3-319-20466-6_29
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DOI: https://doi.org/10.1007/978-3-319-20466-6_29
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