<p>Portfolio optimization is the problem ofsearching foran optimal allocation of wealth to put in the available assets. Since the seminalworkdoneby Markowitz, the problem is codifiedas a two-objective mean-risk optimization problem where the best trade-off solutions (portfolios) between risk (measured by variance) and mean are hunted. Complex measures of risk (e.g., value-at-risk, expected shortfall, semivariance), addedobjective functions (e.g., maximization of skewness, liquidity, dividends) and pragmatic, real-worldconstraints (e.g., cardinality constraints, quantity constraints, minimum transaction lots, class constraints) that are included in recent portfolio selection models, provide many optimization challenges. The resulting portfolio optimizationproblem becomes very hard to be tackledwith exact techniquesas it displaysnonlinearities, discontinuities and high dimensional efficient frontiers. These characteristics prompteda lot ofresearchers to explorethe use of metaheuristics, which are powerful techniquesfor discoveringnear optimal solutions (sometimes the real optimum) for hard optimization problems in acceptable computationaltime. This report provides a briefnoteon the field of portfolio optimization with metaheuristics and concludes that especially Multiobjectivemetaheuristics (MOMHs) provide a natural background for dealing with portfolio selection problems with complex measures of risk (which define non-convex, non-differential objective functions), discrete constraints and multiple objectives.</p>
Numerical methods for mean-risk portfolio optimization
