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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.
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TL;DR: It is shown that the conventional auction, if combined with a suitable day-ahead dispatch of stochastic producers (generally different from their expected production), can substantially increase market efficiency and emulate the advantageous features of the Stochastic optimization ideal, while avoiding its major pitfalls.
120 citations
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TL;DR: Linear programming integer programming graph theory and networks dynamic programming nonlinear programming multiobjective programming stochastic programming heuristic methods.
Abstract: Linear programming integer programming graph theory and networks dynamic programming nonlinear programming multiobjective programming stochastic programming heuristic methods.
120 citations
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TL;DR: In this article, a robust optimal reinsurance and investment problem under Heston's Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and aims to find robust optimal strategies is considered.
Abstract: This paper considers a robust optimal reinsurance and investment problem under Heston’s Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and aims to find robust optimal strategies. The surplus process of the insurer is assumed to follow a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston’s SV model. By adopting the stochastic dynamic programming approach, closed-form expressions for the optimal strategies and the corresponding value functions are derived. Furthermore, a verification result and some technical conditions for a well-defined value function are provided. Finally, some of the model’s economic implications are analyzed by using numerical examples and simulations. We find that ignoring model uncertainty leads to significant utility loss for the AAI. Moreover we propose an alternative model and associated investment strategy which can be considered more adequate under certain finance interpretations, and which leads to significant improvements in our numerical example.
120 citations
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TL;DR: This study applies stochastic programming modelling and solution techniques to planning problems for a consortium of oil companies and involves decisions in both space and time and careful revision of the original deterministic formulation of the DROP model.
Abstract: In this paper we apply stochastic programming modelling and solution techniques to planning problems for a consortium of oil companies. A multiperiod supply, transformation and distribution scheduling problem—the Depot and Refinery Optimization Problem (DROP)—is formulated for strategic or tactical level planning of the consortium's activities. This deterministic model is used as a basis for implementing a stochastic programming formulation with uncertainty in the product demands and spot supply costs (DROPS), whose solution process utilizes the deterministic equivalent linear programming problem. We employ our STOCHGEN general purpose stochastic problem generator to ‘recreate’ the decision (scenario) tree for the unfolding future as this deterministic equivalent. To project random demands for oil products at different spatial locations into the future and to generate random fluctuations in their future prices/costs a stochastic input data simulator is developed and calibrated to historical industry data. The models are written in the modelling language XPRESS-MP and solved by the XPRESS suite of linear programming solvers. From the viewpoint of implementation of large-scale stochastic programming models this study involves decisions in both space and time and careful revision of the original deterministic formulation. The first part of the paper treats the specification, generation and solution of the deterministic DROP model. The stochastic version of the model (DROPS) and its implementation are studied in detail in the second part and a number of related research questions and implications discussed.
120 citations
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30 Sep 1995
TL;DR: This chapter discusses the development of Stochastic Differential Equations and its applications in deterministic and non-deterministic systems.
Abstract: Preface Introduction From Deterministic to Stochastic Linear Control Systems Text Organization and Reading Suggestion MATHEMATICAL PRELIMINARIES Probability and Random Processes Probability, Measure, and Integration Convergence of Random Sequences Random Vectors and Conditional Expectations Second Order Processes and Calculus in Mean Square Exercises References Ito Integrals and Stochastic Differential Equations Markov Processes Orthogonal Increments Processes and the Wiener-Levy Process Ito Integrals and Stochastic Differential Equations Exercises References LINEAR STOCHASTIC CONTROL SYSTEMS: THE DISCRETE-TIME CASE Analysis of Discrete-Time Linear Stochastic Control Systems Analysis of Discrete-Time Causal LTI Systems Analysis of Causal LTI Stochastic Control Systems Analysis of the "State" Description of Controlled Markov Chains State Space Systems and ARMA Models Mathematical Modeling and Applications Exercises References Optimal Estimation for Discrete-Time Linear Stochastic Systems Optimal State Estimation Recursive Optimal Estimation and Kalman Filtering Modified Kalman Filtering Algorithms Exercises References Optimal Control of Discrete-Time Linear Stochastic Systems Introduction Dynamic Programming and LQC Control Problems LQC Optimal Control Problems Adaptive Stochastic Control Exercises References LINEAR STOCHASTIC CONTROL SYSTEMS: THE CONTINUOUS-TIME CASE Continuous-Time Linear Stochastic Control Systems Analysis of Continuous-Time Causal LTI Systems Further Discussion of Markov Processes Dynamic Programming and LQ Control Problems Exercises References Optimal Control of Continuous-Time Linear Stochastic Systems The Continuous-Time LQ Stochastic Control Problem Stochastic Dynamic Programming Innovation Processes and the Kalman-Bucy Filter Optimal Prediction and Smoothing The Separation Principle Exercises References Stability Analysis of Stochastic Differential Equations Stability of Deterministic Systems Stability of Stochastic Systems Stability of Moments Exercises References Appendix Fundamental Real and Functional Analysis Fundamental Matrix Theory and Vector Calculations Martingales References Index
120 citations