Managing financial risk in planning under uncertainty

2010

IMA Journal of Management Mathematics, 2013

This paper addresses the capital budgeting problem under uncertainty. In particular, we propose a multistage stochastic programming model aimed at selecting and managing a project portfolio. The dynamic uncertain evolution of each project value is modelled by a scenario tree over the planning horizon. The model allows the decision maker to revise decisions by decommitting from a given project if it shows a negative performance. Risk is explicitly assessed by defining a mean-risk objective function, where the conditional value at risk is used. A customized branch-and-bound method is also introduced for solving the proposed model. Extensive computational experiments have been carried out to validate the model effectiveness, also in comparison with other possible benchmark policies. The numerical results collected by solving randomly generated instances with the proposed branch-and-bound approach seems to be encouraging.

Computational Management Science, 2009

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0-1 program solving is proposed. Some computational experience is reported.

This paper proposes a new methodology to include financial risk management in the framework of two-stage stochastic programming for energy planning under uncertainties in demands and fuel price. A deterministic mixed integer linear programming formulation is extended to a two-stage stochastic programming model in order to take into account random parameters that have discrete and finite probabilistic distributions. Thus the expected value of the total cost of power generation is minimized, while the carbon emission reduction constraint is satisfied. Furthermore, the so-called conditional value at risk, a risk measure in financial risk management, is incorporated within the framework of two-stage mixed integer programming. The proposed new methodology is implemented in an existing Ontario Power Generation (OPG) fleet with existing technologies and new technologies individually, while reducing carbon emissions under uncertain factors. The new methodology is analyzed under the integrat...

Chemical Engineering and Processing: Process Intensification, 2008

This work proposes a hybrid of stochastic programming (SP) approaches for an optimal midterm refinery planning that addresses three sources of uncertainties: prices of crude oil and saleable products, demands, and yields. An SP technique that utilizes compensating slack variables is employed to explicitly account for constraints' violations to increase model tractability. Four approaches are considered to ensure solution and model robustness: (1) the Markowitz's mean-variance (MV) model to handle randomness in the objective function coefficients by minimizing the variance (economic risk) of the expected value of the random coefficients; (2): the two-stage SP with fixed recourse approach to deal with randomness in the RHS and LHS coefficients of the constraints by minimizing the expected recourse costs due to constraints' violations; (3) incorporation of the MV model within the framework developed in (2) to formulate a mean-risk model that minimizes both the expectation and the operational risk measure of variance of the recourse costs; and (4) reformulation of the model in (3) by adopting mean-absolute deviation (MAD) as the measure of operational risk imposed by the recourse costs for a novel refinery planning application. A representative numerical example is illustrated.

… of Asset and Liability Management: …, 2006

Excellence in 2000. The Center faculty, graduate students, and visitors pursue a broad research agenda that focuses on optimal financial decision making from both the supply side (financial institutions) and the demand side (households and institutional investors). Emphasis is placed on the challenges created for both sides by the globalization and innovations of the financial markets, especially for the economies of pre-accession States as they move towards harmonization with European Union.

Computers & Operations Research, 2012

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse two-stage stochastic programming model, where we specify the conditional-value-at-risk (CVaR) as the risk measure. We construct two decomposition algorithms based on the generic Benders-decomposition approach to solve such problems. Both single-cut and multicut versions of the proposed decomposition algorithms are presented. We adapt the concepts of the value of perfect information (VPI) and the value of the stochastic solution (VSS) for the proposed risk-averse two-stage stochastic programming framework and define two stochastic measures on the VPI and VSS. We apply the proposed model to disaster management, which is one of the research fields that can significantly benefit from risk-averse two-stage stochastic programming models. In particular, we consider the problem of determining the response facility locations and the inventory levels of the relief supplies at each facility in the presence of uncertainty in demand and the damage level of the disaster network. We present numerical results to discuss how incorporating a risk measure affects the optimal solutions and demonstrate the computational effectiveness of the proposed methods.

LE, Sucar, EF, Morales, and J., Hoey (Eds.), Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions. Hershey, Pennsylvania, USA: Information Science Publishing, 2011

In this chapter, we present the multistage stochastic programming framework for sequential decision making under uncertainty and stress its differences with Markov Decision Processes. We describe the main approximation technique used for solving problems formulated in the multistage stochastic programming framework, which is based on a discretization of the disturbance space. We explain that one issue of the approach is that the discretization scheme leads in practice to ill-posed problems, because the complexity of the numerical optimization algorithms used for computing the decisions restricts the number of samples and optimization variables that one can use for approximating expectations, and therefore makes the numerical solutions very sensitive to the parameters of the discretization. As the framework is weak in the absence of efficient tools for evaluating and eventually selecting competing approximate solutions, we show how one can extend it by using machine learning based techniques, so as to yield a sound and generic method to solve approximately a large class of multistage decision problems under uncertainty. The framework and solution techniques presented in the chapter are explained and illustrated on several examples. Along the way, we describe notions from decision theory that are relevant to sequential decision making under uncertainty in general.

Computers & Operations Research, 2009

Australian Journal of Agricultural Economics, 1975

A planning methodology is developed based on Monte Carlo sampling of plans and sorting out inefficient plans according to the rules of stochastic dominance. Illustrations and methodological comparison are made in a context of farm planning under risk, and an application in income stabilization research is indicated.