Threshold Boolean Form for Joint Probabilistic Constraints with Random Technology Matrix

We develop a new modeling and exact solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the … Read more

Construction of Risk-Averse Enhanced Index Funds

We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting … Read more

Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems

optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function (pdBf) representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. We show that … Read more

Mathematical Programming Approaches for Generating p-Efficient Points

Probabilistically constrained problems, in which the random variables are finitely distributed, are non-convex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we … Read more

A VaR Black-Litterman Model for the Construction of Absolute Return Fund-of-Funds

The objective of this study is to construct fund-of-funds (FoF) that follow an absolute return strategy and meet the requirements imposed by the Value-at-Risk (VaR) market risk measure. We propose the VaR-Black Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic … Read more


The ballroom dancing showcases at Fred Astaire East Side Dance Studio in Manhattan are held at least twice a year and provide the students with an environment for socializing, practice, and improvement. The most important part of a showcase organization is the construction of the dance presentations timetable, and, with the number of participants increasing … Read more

Optimization for Simulation: LAD Accelerator

The goal of this paper is to address the problem of evaluating the performance of a system running under unknown values for its stochastic parameters. A new approach called LAD for Simulation, based on simulation and classification software, is presented. It uses a number of simulations with very few replications and records the mean value … Read more


The central objective of this paper is to develop a transparent, consistent, self-contained, and stable country risk rating model, closely approximating the country risk ratings provided by Standard and Poor’s (S&P). The models should be non-recursive, i.e., they should not rely on the previous years’ S&P ratings. The selected set of variables includes not only … Read more

An Exact Solution Approach for Portfolio Optimization Problems under Stochastic and Integer Constraints

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

MIP Reformulations of the Probabilistic Set Covering Problem

In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more