Diffusions for global optimizations
SIAM Journal on Control and Optimization
Diffusion for global optimization in Rn
SIAM Journal on Control and Optimization
A mean-absolute deviation-skewness portfolio optimization model
Annals of Operations Research
Journal of Global Optimization
A Stochastic Algorithm for Constrained Global Optimization
Journal of Global Optimization
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Mean-Variance-Skewness-Kurtosis-based Portfolio Optimization
IMSCCS '06 Proceedings of the First International Multi-Symposiums on Computer and Computational Sciences - Volume 2 (IMSCCS'06) - Volume 02
Linearly Constrained Global Optimization and Stochastic Differential Equations
Journal of Global Optimization
Portfolio Management with Heuristic Optimization (Advances in Computational Management Science)
Portfolio Management with Heuristic Optimization (Advances in Computational Management Science)
Index tracking with constrained portfolios: Research Articles
International Journal of Intelligent Systems in Accounting and Finance Management
Global optimization of the scenario generation and portfolio selection problems
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
A review of recent advances in global optimization
Journal of Global Optimization
Convergence analysis of a global optimization algorithm using stochastic differential equations
Journal of Global Optimization
Steepest ascent hill climbing for portfolio selection
EvoApplications'12 Proceedings of the 2012t European conference on Applications of Evolutionary Computation
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We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (assuming either normally distributed returns or quadratic utility functions) might be too simplifying. The inclusion of higher order moments has therefore been proposed as a possible augmentation of the classical model in order to make it more widely applicable. The resulting problem is non-convex, large scale, and highly relevant in financial optimization. We discuss the solution of the model using two stochastic algorithms. The first algorithm is Differential Evolution (DE). DE is a population based metaheuristic originally designed for continuous optimization problems. New solutions are generated by combining up to four existing solutions plus noise, and acceptance is based on evolutionary principles. The second algorithm is based on the asymptotic behavior of a suitably defined Stochastic Differential Equation (SDE). The SDE consists of three terms. The first term tries to reduce the value of the objective function, the second enforces feasibility of the iterates, while the third adds noise in order to enable the trajectory to climb hills.