Bernardo Pagnoncelli

• PhD
• Professor at SKEMA Business School

The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates th...

Two-stage risk-averse stochastic programming goes beyond the classical expected value framework and aims at controlling the variability of the cost associated with different outcomes based on a choice of a risk measure. In this paper, we study stochastic decomposition (SD) for solving large-scale risk-averse stochastic linear programs with deviatio...

Context-Sensitive Simulation-Based Decisions When There Is No Time to Simulate Stochastic simulation is a powerful tool for discovering system design decisions that are the best possible (optimal) when averaged over real-world uncertainty. However, in applications such as personalized medicine and web content optimization, even better decisions can...

PolieDRO is a novel analytics framework for classification and regression that harnesses the power and flexibility of data-driven distributionally robust optimization (DRO) to circumvent the need for regularization hyperparameters. Recent literature shows that traditional machine learning methods such as SVM and (square-root) LASSO can be written a...

Over the last two decades, coherent risk measures have been well studied as a principled, axiomatic way to characterize the risk of a random variable. Because of this axiomatic approach, coherent risk measures have a number of attractive features for computation, and they have been integrated into a variety of stochastic programming algorithms, inc...

Features, or contextual information, are additional data than can help predicting asset returns in financial problems. We propose a mean-risk portfolio selection problem that uses contextual information to maximize expected returns at each time period, weighing past observations via kernels based on the current state of the world. We consider yearl...

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is...

In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits gen...

The method of continuous gas lift has been commonly used in the oil industry to enhance production. Existing optimization models consider an approximate performance curve anchored by production test data, often disregarding reservoir uncertainty. We propose a robust optimization model that jointly considers the most recent data and an uncertainty s...

Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value; constraints enforce geotechnical precedence between activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic sched...

In 1964, Kenneth Lane proposed an algorithm to optimize the production schedule of a single-metal, single-processor open pit mine. For this, he proposed a policy based on varying, over time, the so-called “cutoff grade”—or grade threshold used to determine if extracted material should be ore (processed material) or waste (thrown away). Lane’s algor...

Portfolio selection problems have been thoroughly studied under the risk-and-return paradigm introduced by Markowitz. However, the usefulness of this approach has been hindered by some practical considerations that have resulted in poorly diversified portfolios, or, solutions that are extremely sensitive to parameter estimation errors. In this work...

Defined contribution (DC) pension plans have been gaining ground in the last 10–20 years as the preferred system for many countries and other agencies, both private and public. The central question for a DC plan is how to invest in order to reach the participant's retirement goals. Given the financial illiteracy of the general population, it is com...

We propose a class of partially observable multistage stochastic programs and describe an algorithm for solving this class of problems. We provide a Bayesian update of a belief-state vector, extend the stochastic programming formulation to incorporate the belief state, and characterize saddle-function properties of the corresponding cost-to-go func...

The alternate direction method of multipliers (ADMM) has received significant attention recently as a powerful algorithm to solve convex problems with a block structure. The vast majority of applications focus on deterministic problems. In this paper we show that ADMM can be applied to solve two-stage stochastic programming problems, and we propose...

Continuous gas lift is a popular method to enhance productivity in offshore oil platforms. We propose a steady-state two-stage stochastic programming model to maximize production, where the first-stage injection level determines the production potential, while recourse actions ensure capacity and platform constraints for each uncertainty realizatio...

We propose a multistage stochastic programming model to optimally allocate cargo to the passengers network in order to maximize profit, taking into account incomes, costs and penalties for not delivering cargo that was previously accepted. Flights have a discrete number of possible capacity outcomes, with known probabilities, and uncertainty is rep...

Among the many sources of uncertainty in mining are production incidents: these can be strikes, environmental issues, accidents, or any kind of event that disrupts production. In this work, we present a strategic mine-planning model that takes into account these types of incidents, as well as random prices. When confronted by production difficultie...

We propose an algorithm based on infeasible irreducible subsystems (IIS) to solve binary linear chance-constrained problems with random technology matrix. By leveraging on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete domain is used to guide us efficiently in th...

Mexico and Chile have Defined Contributions (DC) pension systems. In both cases affiliates are offered several investment funds with, allegedly, different risk-return profiles. Analyzing actual return data for the April 2008-March 2018 period, and using a number of risk-and return-related metrics, we reach quite different conclusions in relation to...

In defined contribution (DC) pension schemes, the regulator usually imposes asset allocation constraints (minimum and maximum limits by asset class) in order to create funds with different risk–return profiles. In this article, we challenge this approach and show that such funds can exhibit erratic risk–return profiles that deviate significantly fr...

We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers' reservation prices. At the upper-level of the Stackelberg game, the aggregator o...

In this paper we discuss scenario reduction methods for risk-averse stochastic optimization problems. Scenario reduction techniques have received some attention in the literature and are used by practitioners, as such methods allow for an approximation of the random variables in the problem with a moderate number of scenarios, which in turn make th...

In de�ned contribution (DC) pension schemes, the regulator usually imposes asset allocation constraints (minimum and maximum limits by asset class) in order to create funds with different risk-return profiles. In this article, we challenge this approach and show that such funds can exhibit erratic risk-return profiles that deviate significantly fro...

We propose a two-step hybrid investment strategy suitable for pension funds. Our method consists of an active component (an optimization-based approach to decide the asset allocation), followed by a passive strategy (an index-based approach). We test our strategy with data from the Chilean pension system using two different risk metrics and we show...

We study the exploitation of a one species, multiple stand forest plantation when timber price is governed by a stochastic process. Our model is a stochastic dynamic program with a weighted mean-risk objective function, and our main risk measure is the Conditional Value-at-Risk. We consider two stochastic processes, geometric Brownian motion and Or...

In air cargo transportation, capacity can be reserved via allotment, which are long-term contracts with fixed price, and free, which is the space not assigned to allotment contracts. In this later case, reservations are made closer to the departure date, and normally higher tariffs are charged. The demand, the tariff, and the show-up rate for the f...

We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sam...

We discuss the incorporation of risk measures into multistage stochastic programs. While much attention has been recently devoted in the literature to this type of model, it appears that there is no consensus on the best way to accomplish that goal. In this paper, we discuss pros and cons of some of the existing approaches. A key notion that must b...

Credit risk derivatives and securitization techniques are difficult topics to teach. Most students have preconceived ideas some of them quite wrong. And frequently students feel there is almost something like "black magic" behind the concept that one can create Aaa securities out of risky assets. Moreover, the fact that credit derivatives played an...

We propose a model to assess the credit risk features of fixed income portfolios assuming they can be characterized by two parameters: their default probability and their default correlation. We rely on explicit expressions to assess their credit risk and demonstrate the benefits of our approach in a complex leveraged structure example. We show tha...

We extend the classic Mitra and Wan forestry model by assuming that prices follow a geometric Brownian motion. We move one step further in the model with stochastic prices and include risk aversion in the objec-tive function. We prove that, as in the deterministic case, the optimal program is periodic both in the risk neutral and risk averse framew...

In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is...

Securitization is a difficult topic to teach. Most students have preconceived ideas about it. Some of them are quite wrong. And frequently many students feel that there is almost something like “black magic” behind the concept that one can create AAA-securities out of risky assets. Additionally, the fact that securitization played an important role...

We consider the scenario approach for chance constrained programming problems. Building on existing theoretical results, effective and readily applicable methodologies to achieve suitable risk-return trade-offs are developed in this paper. Unlike other approaches, that require solving non-convex optimization problems, our methodology consists of so...

We consider the problem of determining the minimal requirement one must establish in order to meet a series of future random payments. It is shown in a very general setting that this problem can be recast as a chance constrained model and how the technique of Sample Average Approximation can be employed to find solutions. We also use comonotonic th...

In this paper we study the dynamical formulation of the n-firm Cournot oligopoly model and variations. We consider both discrete and continuous cases and discuss its stability as well as its long-term behavior. As these resulting models are linear, we propose the use of techniques from linear algebra such as Shermann-Morrison's formula and Sylveste...

We study the effect of transaction costs in collective investment schemes such as investment funds or investments pools. We consider a group of partners or independent investors who contributed for a project with different amounts and now need to get even through financial transfers which involve transaction costs. Those transfers have to be made i...

We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed t...

The Cournot oligopoly model was introduced in the 19th century, and has been extensively studied since then. Most textbooks in economics treat simplified cases only, with 2 or 3 firms competing for the market. For the general case, some simple situations have been treated in [6] and [2]. Here we show how the use of linear algebra in a level above u...

The purpose of these notes is to present computational advances in the analysis of the hy- drothermal scheduling problem studied in ( 2). In the first part we briefly summarize the main results of the original paper, stating the main theorems without proofs. In the second part we present the computer program wxHSP, designed to obtain numerical solu...

We study approximations of chance constrained problems. In par-ticular, we consider the Sample Average Approximation (SAA) ap-proach and discuss convergence properties of the resulting problem. A method for constructing bounds for the optimal value of the considered problem is discussed and we suggest how one should tune the under-lying parameters...

In this paper we study the well-known linear system of differential equations in the plane. Instead of considering a fixed matrix A, we assume that its entries are random variables and we argue about the probability of the origin be each of the fixed points, such as saddle, node, etc. The problem was suggested by Steven Strogatz in his book (8). We...