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Application of multistage stochastic programs solved in parallel in portfolio management

PARALLEL COMPUTING 2008年第6-8期34卷 469-485页

作者： Lucka, Maria Melichercik, Igor Halada, Ladislav Univ Trnava Fac Educ Trnava 91843 Slovakia Comenius Univ Fac Math Phys & Informat Dept Appl Math & Stat Bratislava 84248 Slovakia Slovak Acad Sci Inst Informat Bratislava 84237 Slovakia Univ Vienna Inst Comp Sci A-1090 Vienna Austria

We present a multistage model for allocation of financial resources to bond indices in different currencies. The model was tested on historical data of interest and exchange rates. We compare a two-stage and a three-stage stochastic programming model from a financial performance point of view. For solving two-stage and three-stage stochastic programs the interior point method (IPM) in the frame of the primal-dual path following formulation is used. An application of the Birge and Qi factorization to the IPM allows decomposition of large linear system to smaller blocks allowing thus to solve it in parallel. The parallel code is written in the Fortran programming language, using the message passing interface (MPI) for communication. Parallel and financial performance is illustrated on experiments executed on the IBM 1350 Linux cluster. (C) 2008 Elsevier B.V. All rights reserved.

关键词： portfolio management interior point method parallel computing large-scale optimization multistage stochastic programming

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Dynamic reverse supply chain network design under uncertainty: mathematical modeling and solution algorithm

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2022年第5期29卷 3161-3189页

作者： Jeihoonian, Mohammad Zanjani, Masoumeh Kazemi Gendreau, Michel Concordia Univ Dept Mech Ind & Aerosp Engn Montreal PQ H3G 1M8 Canada Polytech Montreal Dept Math & Ind Engn Montreal PQ H3C 3A7 Canada Interuniv Res Ctr Enterprise Networks Logist & Tr Montreal PQ H3C 3A7 Canada

Motivated by the recovery of modular-structured products, this study addresses the flexible design of a reverse supply chain (RSC) over a planning horizon while incorporating the dynamic uncertain behavior of product returns. The stochastic parameter is modeled as a scenario tree and therefore the concerned problem is formulated as a multistage mixed-integer stochastic program. To alleviate the computational complexity of the proposed model, it is decomposed into smaller scenario cluster submodels associated with a number of subtrees that share a certain number of predecessor nodes in the original scenario tree. The submodels are coordinated into an implementable solution via a Lagrangian-progressive hedging-based method that employs a viable Benders decomposition based algorithm for solving each scenario cluster submodel. Based on a realistic scale case, computational results indicate the superiority of the proposed flexible dynamic RSC design model compared to the existing models. Results also demonstrate the efficiency of the proposed solution approach.

关键词： flexible reverse supply chain design multistage stochastic programming scenario clustering decomposition Benders decomposition

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Risk-Based Reserve Scheduling for Active Distribution Networks Based on an Improved Proximal Policy Optimization Algorithm

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IEEE ACCESS 2023年 11卷 15211-15228页

作者： Li, Xiaoyu Han, Xueshan Yang, Ming Shandong Univ Key Lab Power Syst Intelligent Dispatch & Control Minist Educ Jinan 250061 Peoples R China

Achieving the coordinated optimization of tie-line reserve and energy storage on two timescales is a key issue in reserve scheduling for active distribution networks. To effectively manage the uncertainty related to renewable energy, we propose risk-based reserve scheduling for active distribution networks based on an improved proximal policy optimization algorithm. The reserve scheduling for active distribution networks is constructed as a two-scale multistage stochastic programming model, in which intraday real-time operation is constructed as a multi-stage stochastic programming model. With the help of more accurate and realistic intraday operation scenario simulation, the energy storage can be fully utilized to improve the system's ability to climb and peak, reduce the reserve pressure of the main network, and achieve the purpose of improving the flexibility of system operation. An improved proximal policy optimization algorithm is proposed to solve optimization problems in a model-free manner while effectively handling conditional value-at-risk constraints. The effectiveness of the proposed risk-based reserve scheduling for active distribution networks based on an improved proximal policy optimization algorithm is verified by a modified IEEE33 case.

关键词： Optimization Renewable energy sources Reactive power Costs Power systems Active distribution networks Deep learning Reinforcement learning Active distribution network multistage stochastic programming conditional value-at-risk reserve scheduling deep reinforcement learning

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Short-term optimal operation of water systems using ensemble forecasts

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ADVANCES IN WATER RESOURCES 2014年 71卷 200-208页

作者： Raso, L. Schwanenberg, D. van de Giesen, N. C. van Overloop, P. J. Delft Univ Technol Delft Netherlands IRSTEA F-34196 Montpellier France Deltares Fdn Delft Netherlands Univ Duisburg Essex Duisburg Germany

Short-term water system operation can be realized using Model Predictive Control (MPC). MPC is a method for operational management of complex dynamic systems. Applied to open water systems, MPC provides integrated, optimal, and proactive management, when forecasts are available. Notwithstanding these properties, if forecast uncertainty is not properly taken into account, the system performance can critically deteriorate. Ensemble forecast is a way to represent short-term forecast uncertainty. An ensemble forecast is a set of possible future trajectories of a meteorological or hydrological system. The growing ensemble forecasts' availability and accuracy raises the question on how to use them for operational management. The theoretical innovation presented here is the use of ensemble forecasts for optimal operation. Specifically, we introduce a tree based approach. We called the new method Tree-Based Model Predictive Control (TB-MPC). In TB-MPC, a tree is used to set up a multistage stochastic programming, which finds a different optimal strategy for each branch and enhances the adaptivity to forecast uncertainty. Adaptivity reduces the sensitivity to wrong forecasts and improves the operational performance. TB-MPC is applied to the operational management of Salto Grande reservoir, located at the border between Argentina and Uruguay, and compared to other methods. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Operational water management Short term reservoir management Model Predictive Control Ensemble forecast multistage stochastic programming Robustness

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An interval multistage classified model for regional inter- and intra-seasonal water management under uncertain and nonstationary condition

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AGRICULTURAL WATER MANAGEMENT 2017年 191卷 98-112页

作者： Chen, Shu Shao, Dongguo Tan, Xuezhi Gu, Wenquan Lei, Caixiu Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan Hubei Peoples R China Univ Alberta Dept Civil & Environm Engn Edmonton AB Canada Hubei Prov Water Resources & Hydropower Planning Wuhan Hubei Peoples R China

In regional water management, various uncertainties such as randomness, non-stationarities, dynamics and complexities, lead to difficulties for water managers. To deal with the above problems, a new methodology is proposed by introducing two methods nonstationary analysis, where the generalized additive model is selected to analyze and fit the distribution of water inflow;and model optimization, where an interval multistage water classified-allocation model (IMWCA) is formulated to optimally allocate the available water. By incorporating multistage stochastic programming, interval parameter programming and classification thought, the IMWCA model can tackle both stochastic and imprecise uncertainties, realize inter-seasonal dynamic allocation, and address the complexity of various water users. The methodology is applied to the Zhanghe Irrigation District to optimize water allocation for municipality, industry, hydropower and agriculture among winter, spring, summer and autumn. The Zhanghe Reservoir seasonal inflow is found to be nonstationary for all the seasons and can be well fitted by the corresponding distributions, showing the sense of nonstationary analysis. Additionally, the comparison with the other model demonstrates the need for classification. From the results, municipality and industry are more competitive than hydropower. The Dongbao, Dangyang and Zhanghe districts have a higher priority than the Jingzhou and Shayang districts for irrigation water. Water requirements are more likely to be satisfied in autumn. These solutions of optimal targets and optimal water allocation are valuable for optimizing inter- and intra-seasonal water resource allocation under uncertainty. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Classification Interval programming Nonstationary analysis multistage stochastic programming Uncertainty Inter-seasonal water management

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A branch and bound algorithm to solve large-scale multistage stochastic programs with endogenous uncertainty

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AICHE JOURNAL 2018年第4期64卷 1262-1271页

作者： Christian, Brianna Cremaschi, Selen Auburn Univ Dept Chem Engn Samuel Ginn Coll Engn Auburn AL 36849 USA

The growth in computation complexity of multistage stochastic programs (MSSPs) with problem size often prevents its application to real-world size problems. We present two variants of branch-and-bound algorithm, which reduce the resource requirements for the generation and solution of large-scale MSSPs with endogenous uncertainty. Both variants use Knapsack-problem based Decomposition Algorithm (Christian and Cremaschi, Comput Chem Eng. 2015;74:34-47) to generate feasible solutions and primal bounds. First variant (PH-KDA) uses a progressive hedging dual-bounding approach;the second (OSS-KDA) solves the MSSP removing all nonanticipativity constraints. Both variants were used to solve several instances of the pharmaceutical clinical trial planning problem. The first iteration of both algorithms provides a feasible solution, and a primal bound and a dual bound for the problem. Although the dual-bounds of OSS-KDA were generally weaker than PH-KDA, they are generated considerably faster. For the seven-product case the OSS-KDA generated a solution with a gap of 9.92% in 115 CPU seconds. (c) 2017 American Institute of Chemical Engineers AIChE J, 64: 1262-1271, 2018

关键词： multistage stochastic programming pharmaceutical clinical trial planning progressive hedging branch and bound endogenous uncertainty

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Retirement planning in individual asset-liability management

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2012年第4期23卷 365-396页

作者： Consigli, Giorgio Iaquinta, Gaetano Moriggia, Vittorio di Tria, Massimo Musitelli, Davide Univ Bergamo Dept Math Stat & Comp Sci Bergamo Italy Allianz Investment Management Milan Italy

Increasing financial pressure on State-controlled pension systems has caused, over the last two decades or so, an unprecedented effort by private pension funds (PFs) and insurance companies to issue new types of retirement vehicles. This article investigates the effects of such widespread phenomenon from the perspective of individual asset-liability management. A multistage stochastic programming problem has been formulated with investment opportunities including PFs, unit-linked contracts and variable life annuities. The introduction of a specific risk measure with respect to a desirable retirement income stream and a planning horizon spanning the entire individuals' working life helps to analyse the implications of observed market dynamics on retirement strategies. We present comparative results focusing on the retirement planning problem for three representative individuals carrying different time horizons but common retirement goals. The results show the benefits over traditional pension accumulation plans of dynamic strategies based on mixed portfolios of retirement products.

关键词： multistage stochastic programming asset-liability management individual retirement planning variable life annuities private pension plans

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STABILITY OF A CLASS OF RISK-AVERSE multistage stochastic PROGRAMS AND THEIR DISTRIBUTIONALLY ROBUST COUNTERPARTS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第5期17卷 2415-2440页

作者： Jiang, Jie Chen, Zhiping Hu, He Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Xian Int Acad Math & Math Technol Ctr Optimizat Tech & Quantitat Finance Xian 710049 Shaanxi Peoples R China

In this paper, we consider the quantitative stability of a class of risk-averse multistage stochastic programs, whose objective functions are defined by multi-period pth order lower partial moments (LPM) with given targets, and their distributionally robust counterparts. We first derive the upper bounds of feasible solutions as preliminaries. Then, by employing calm modifications, the quantitative stability results are obtained under a special measurable perturbation of stochastic process, which extend the present results under risk-neutral cases to risk-averse ones. Moreover, we recast the risk-averse model by probability measures of stochastic process, and obtain new quantitative stability estimations on the basis of proper probability metrics under the general perturbation of stochastic process. Finally, motivated by the availability of only partial information about probability measures, we further consider the distributionally robust counterpart of our recasting model, and establish the discrepancy of optimal values with respect to the perturbation of ambiguity sets.

关键词： risk-averse quantitative stability LPM distributionally robust multistage stochastic programming

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Measuring risk for income streams

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第1-2期32卷 161-178页

作者： Pflug, GC Ruszczynski, A Univ Vienna Dept Stat & Decis Support Syst A-1090 Vienna Austria Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08854 USA Rutgers State Univ RUTCOR Piscataway NJ 08854 USA

A measure of risk is introduced for a sequence of random incomes adapted to some filtration. This measure is formulated as the optimal net present value of a stream of adaptively planned commitments for consumption. The new measure is calculated by solving a stochastic dynamic linear optimization problem which, for finite filtrations, reduces to a deterministic linear programming problem. We analyze properties of the new measure by exploiting the convexity and duality structure of the stochastic dynamic linear problem. The measure depends on the full distribution of the income process (not only on its marginal distributions) as well as on the filtration, which is interpreted as the available information about the future. The features of the new approach are illustrated by a numerical example.

关键词： dynamic risk measure multistage stochastic programming multiperiod mean-risk models value of perfect information conditional value at risk

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Solving constrained consumption-investment problems by decomposition algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期319卷 292-302页

作者： Pagnoncelli, Bernardo K. Homem-de-Mello, Tito Lagos, Guido Castaneda, Pablo Garcia, Javier Univ Cote Azur SKEMA Business Sch Ave Willy Brandt F-59777 Lille France Univ Adolfo Ibanez Sch Business Ave Diagonal Torres 2640 Santiago 7941169 Chile Univ Adolfo Ibanez Fac Engn & Sci Padre Hurtado 750 Vina Del Mar 2340000 Chile ACHS Fac Sci & Engn Ramon Carnicer 163 Santiago Chile

Consumption-investment problems with maximizing utility agents are usually considered from a theoretical viewpoint, aiming at closed-form solutions for the optimal policy. However, such an approach requires that the model be relatively simple: even the inclusion of nonnegativity constraints can prevent the derivation of explicit solutions. In such cases, it is necessary to solve the problem numerically, but standard dynamic programming algorithms can only solve small problems due to the curse of dimensionality. In this paper, we adapt the stochastic Dual Dynamic programming (SDDP) algorithm to solve dynamic constrained consumption-investment problems with stochastic labor income numerically. Unlike classical dynamic programming approaches, SDDP allows us to analyze problems with multiple assets, and an internal sampling procedure allows the problems to have a very large, or even infinite, number of scenarios. We start with a simpler problem for which a closed-form solution is known and compare it to the optimal policy obtained by SDDP. We then illustrate the flexibility of our approach by solving a defined contribution pension fund problem with multiple assets, for which no closed-form solution is available.

关键词： Finance Consumption-investment problems multistage stochastic programming Decomposition algorithms

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