We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration … Read more
We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functions. Citation Preprint Article Download View Optimization of Convex Risk Functions
This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and … Read more
We provide two new, simple proofs of Afriat’s celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of Revealed Preference. Citation Technical Report No. 1381, School of Operations … Read more
We show that a simple genralization of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley(1962), yeilds outcomes for a generalized marriage problem, which are necessarily stable. We also show, that any outcome of this prcedure is Weakly Pareto Optimal for Men, i.e., there is no other outcome which all men prefer … Read more
The nearest \cm\ problem is to find a positive semidefinite matrix with unit diagonal that is nearest in the Frobenius norm to a given symmetric matrix $A$. This problem can be formulated as an optimization problem with a quadratic objective function and semidefinite programming constraints. Using such a formulation, we derive and test a primal-dual … Read more
Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is … Read more
This paper considers robust optimization to cope with uncertainty about the stock return process in one period portfolio selection problems involving options. The ro- bust approach relates portfolio choice to uncertainty, making more cautious portfolios when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlyings and show that … Read more
The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. … Read more
The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these … Read more