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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
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Book
18 Jun 2009
TL;DR: In this article, the authors provide a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward Stochastic differential equations, and martingale duality methods.
Abstract: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

715 citations

Journal ArticleDOI
TL;DR: Particular emphasis will be placed on estimation of rare events and on integration of the associated performance function into stochastic optimization programs.

710 citations

Journal ArticleDOI
TL;DR: This study proposes a two-stage stochastic programming model to plan the transportation of vital first-aid commodities to disaster-affected areas during emergency response, and a multi-commodity, multi-modal network flow formulation is developed to describe the flow of material over an urban transportation network.
Abstract: This study proposes a two-stage stochastic programming model to plan the transportation of vital first-aid commodities to disaster-affected areas during emergency response. A multi-commodity, multi-modal network flow formulation is developed to describe the flow of material over an urban transportation network. Since it is difficult to predict the timing and magnitude of any disaster and its impact on the urban system, resource mobilization is treated in a random manner, and the resource requirements are represented as random variables. Furthermore, uncertainty arising from the vulnerability of the transportation system leads to random arc capacities and supply amounts. Randomness is represented by a finite sample of scenarios for capacity, supply and demand triplet. The two stages are defined with respect to information asymmetry, which discloses uncertainty during the progress of the response. The approach is validated by quantifying the expected value of perfect and stochastic information in problem instances generated out of actual data.

696 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the combined optimization of a wind farm and a pumped-storage facility from the point of view of a generation company in a market environment, and formulated the optimization model as a two-stage stochastic programming problem with two random parameters: market prices and wind generation.
Abstract: One of the main characteristics of wind power is the inherent variability and unpredictability of the generation source, even in the short-term. To cope with this drawback, hydro pumped-storage units have been proposed in the literature as a good complement to wind generation due to their ability to manage positive and negative energy imbalances over time. This paper investigates the combined optimization of a wind farm and a pumped-storage facility from the point of view of a generation company in a market environment. The optimization model is formulated as a two-stage stochastic programming problem with two random parameters: market prices and wind generation. The optimal bids for the day-ahead spot market are the ldquohere and nowrdquo decisions while the optimal operation of the facilities are the recourse variables. A joint configuration is modeled and compared with an uncoordinated operation. A realistic example case is presented where the developed models are tested with satisfactory results.

674 citations

Book
01 Jan 1976
TL;DR: In this article, the authors present a model for single-stage SLP models with Probability Functions, Quantile Functions, Value at Risk, Models Based on Expectation, Models Built with Deviation Measures, Modeling Risk and Opportunity, Risk Measures.
Abstract: Basics.- Introduction.- Linear Programming Prerequisites.- Nonlinear Programming Prerequisites.- Single-stage SLP Models.- Introduction.- Models involving Probability Functions.- Quantile Functions, Value at Risk.- Models Based on Expectation.- Models Built with Deviation Measures.- Modeling Risk and Opportunity.- Risk Measures.- Multi-stage SLP Models.- The General SLP with Recourse.- The Two-stage SLP.- The Multi-stage SLP.- Algorithms.- Models with Probability Functions.- Models with Quantile Functions.- Models Based on Expectation.- Models with Deviation Measures.- Two-stage Recourse Problems.- Multi-stage Recourse Problems.- Modeling Systems for SLP.- Bibliography.

663 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532