We develop a multi-stage stochastic programming model for international portfolio management in a dynamic setting. We model uncertainty in asset prices and exchange rates in terms of scenario trees that reflect the em...
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We develop a multi-stage stochastic programming model for international portfolio management in a dynamic setting. We model uncertainty in asset prices and exchange rates in terms of scenario trees that reflect the empirical distributions implied by market data. The model takes a holistic view of the problem. It considers portfolio rebalancing decisions over multiple periods in accordance with the contingencies of the scenario tree. The solution jointly determines capital allocations to international markets, the selection of assets within each market, and appropriate currency hedging levels. We investigate the performance of alternative hedging strategies through extensive numerical tests with real market data. We show that appropriate selection of currency forward contracts materially reduces risk in international portfolios. We further find that multi-stage models consistently outperform single-stage models. Our results demonstrate that the stochastic programming framework provides a flexible and effective decision support tool for international portfolio management. (C) 2006 Elsevier B.V. All rights reserved.
We show how to extend the demand-planning stage of the sales-and-operations-planning (S&OP) process with a spreadsheet implementation of a stochastic programming model that determines the supply requirement while ...
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We show how to extend the demand-planning stage of the sales-and-operations-planning (S&OP) process with a spreadsheet implementation of a stochastic programming model that determines the supply requirement while optimally trading off risks of unmet demand, excess inventory, and inadequate liquidity in the presence of demand uncertainty. We first present the model that minimizes the weighted sum of respective conditional value-at-risk (cVaR) metrics over demand scenarios in the form of a binomial tree. The output of this model is the supply requirement to be used in the supply-planning stage of the S&OP process. Next we show how row-and-column aggregation of the model reduces its size from exponential (2(T)) in the number of time periods T in the planning horizon to merely square (T-2). Finally, we demonstrate the tractability of this aggregated model in an Excel spreadsheet implementation with a numerical example with 26 time periods. Journal of the Operational Research Society (2011) 62, 526-536. doi:10.1057/jors.2010.93 Published online 4 August 2010
Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of...
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Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation of decision stages, discretization of the probability space, and reparameterization of the decision space. We report on numerical results and discuss analytically tractable limiting cases. (C) 2009 Elsevier Ltd. All rights reserved.
The theory on the traditional sample average approximation (SAA) scheme for stochastic programming (SP) dictates that the number of samples should be polynomial in the number of problem dimensions in order to ensure p...
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The theory on the traditional sample average approximation (SAA) scheme for stochastic programming (SP) dictates that the number of samples should be polynomial in the number of problem dimensions in order to ensure proper optimization accuracy. In this paper, we study a modification to the SAA in the scenario where the global minimizer is either sparse or can be approximated by a sparse solution. By making use of a regularization penalty referred to as the folded concave penalty (FCP), we show that, if an FCP-regularized SAA formulation is solved locally, then the required number of samples can be significantly reduced in approximating the global solution of a convex SP: the sample size is only required to be poly-logarithmic in the number of dimensions. The efficacy of the FCP regularizer for nonconvex SPs is also discussed. As an immediate implication of our result, a flexible class of folded concave penalized sparse M-estimators in high-dimensional statistical learning may yield a sound performance even when the problem dimension cannot be upper-bounded by any polynomial function of the sample size.
We present a multi-period stochastic mixed integer programming model for power generation scheduling in a day-ahead electricity market. The model considers various scenarios and integrates the idea of reserve shortage...
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We present a multi-period stochastic mixed integer programming model for power generation scheduling in a day-ahead electricity market. The model considers various scenarios and integrates the idea of reserve shortage pricing in real time. Instead of including all the possible scenarios, we parsimoniously select a certain number of scenarios to limit the size of the model. As realistic size models are still intractable for exact methods, we propose a heuristic solution methodology based on scenario-rolling that is capable of finding good quality feasible solutions within reasonable computation time.
A stochastic programming formulation is developed for determining the optimal placement of gas detectors in petrochemical facilities. FLACS, a rigorous gas dispersion package, is used to generate hundreds of scenarios...
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A stochastic programming formulation is developed for determining the optimal placement of gas detectors in petrochemical facilities. FLACS, a rigorous gas dispersion package, is used to generate hundreds of scenarios with different leak locations and weather conditions. Three problem formulations are investigated: minimization of expected detection time, minimization of expected detection time including a coverage constraint, and a placement based on coverage alone. The extensive forms of these optimization problems are written in Pyomo and solved using CPLEX. A sampling procedure is used to find confidence intervals on the optimality gap and quantify the effectiveness of detector placements on alternate subsamples of scenarios. Results show that the additional coverage constraint significantly improves performance on alternate subsamples. Furthermore, both optimization-based approaches dramatically outperform the coverage-only approach, making a strong case for the use of rigorous dispersion simulation coupled with stochastic programming to improve the effectiveness of these safety systems. (C) 2012 Published by Elsevier Ltd.
In this paper, we introduce the multistage stochastic program with fuzzy probability distribution. We focus on the case where fuzzy probability distribution is defined by (triangular) fuzzy numbers. We extend Ben Abde...
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In this paper, we introduce the multistage stochastic program with fuzzy probability distribution. We focus on the case where fuzzy probability distribution is defined by (triangular) fuzzy numbers. We extend Ben Abdelaziz and Masri [stochastic programming with fuzzy linear partial information on probability distribution, European Journal Operational Research 162 (2005) 619-629] solution strategy, for the two-stage stochastic program with fuzzy probability distribution, to solve the multistage model. The proposed solution strategy is based on two transformation steps. In the first step, the fuzzy transformation step, we propose to use the X-cut defuzzification technique. The level cc relates to the DM credibility degree on information sources. This step ends with a certainty equivalent program. In the second step, the stochastic transformation step, we decompose the certainty equivalent program based on a minimax approach. The obtained problem is then solved using a modified version of the nested decomposition method. The modification on the nested decomposition method concerns the way in which we generate optimal constraints. The modified nested decomposition algorithm may be used to solve the multistage problem with interval probability distribution. (C) 2008 Elsevier B.V. All rights reserved.
In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneo...
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In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneously taking into account three important issues: (i) the model explicitly incorporates uncertainty in the airport capacities;(ii) it also considers the trade-off between airport arrivals and departures, which is a crucial issue in any hub airport;and (iii) it takes into account the interactions between different hubs. The level of aggregation proposed for the mathematical model allows us to solve realistic size instances with a commercial solver on a PC. Moreover it allows us to compute solutions which are perfectly consistent with the Collaborative Decision-Making (CDM) procedure in ATFM, widely adopted in the USA and which is currently receiving a lot of attention in Europe. In fact, the proposed model suggests the number of flights that should be delayed, a decision that belongs to the ATFM Authority, rather than assigning delays to individual aircraft. (C) 2011 Elsevier B.V. All rights reserved.
To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The unce...
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To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the "Curse of Dimensionality" of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.
We consider multistage stochastic programs, in which decisions can adapt over time, (i.e., at each stage), in response to observation of one or more random variables (uncertain parameters). The case that the time at w...
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We consider multistage stochastic programs, in which decisions can adapt over time, (i.e., at each stage), in response to observation of one or more random variables (uncertain parameters). The case that the time at which each observation occurs is decision-dependent, known as stochastic programming with endogeneous observation of uncertainty, presents particular challenges in handling non-anticipativity. Although such stochastic programs can be tackled by using binary variables to model the time at which each endogenous uncertain parameter is observed, the consequent conditional non-anticipativity constraints form a very large class, with cardinality in the order of the square of the number of scenarios. However, depending on the properties of the set of scenarios considered, only very few of these constraints may be required for validity of the model. Here we characterize minimal sufficient sets of non-anticipativity constraints, and prove that their matroid structure enables sets of minimum cardinality to be found efficiently, under general conditions on the structure of the scenario set.
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