In this paper, we study the pricing problem for the class of multiasset European options with piecewise linear convex payoff in the asset prices. We derive a simple upper bound on the price of this option by constructing a static super-replicating portfolio using cash and options on smaller subsets of assets. The best upper bound … Read more
In this paper a covering model for locating facilities with time-dependent demand is introduced. Not only the facility locations, but also the instants at which such facilities become operative, are considered as decision variables in order to determine the maximal-profit decision. Expressed as a mixed nonlinear integer program, structural properties are derived for particular demand … Read more
We present experimental results on portfolio optimization problems with return errors under the robust optimization framework. We use several a histogram-like model for return deviations, and a model that allows correlation among errors, together with a cutting-plane algorithm which proves effective for large, real-life data sets. CitationColumbia Center for Financial Engineering Report 2007-01 Columbia University, … Read more
In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents … Read more
The robust portfolio selection problems have recently been studied by several researchers (e.g., see \cite{GoIy03,ErGoIy04,HaTu04,TuKo04}). In their work, the “separable” uncertainty sets of the problem parameters (e.g., mean and covariance of the random returns) were considered. These uncertainty sets share two common drawbacks: i) the actual confidence level of the uncertainty set is unknown, and … Read more
Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which … Read more
It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical mean-variance theory. The first model is an extension … Read more
We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model of the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle … Read more
In this paper we show that for discrete concave functions, a local maximum need not be a global maximum. We also provide examples of discrete concave functions where this coincidence holds. As a direct consequence of this, we can establish the equivalence of local and global profit maximizers for an equivalent well-behaved production function that … Read more
Sparse PCA seeks approximate sparse “eigenvectors” whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NP-hard and yet it is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality … Read more