Topic
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: In this paper, a stochastic programming procedure is proposed for managing asset/liability portfolios with interest rate contingent claims, using scenario generation to combine deterministic dedication techniques with stochastically duration matching methods, and providing the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes.
Abstract: Drawing on recent developments in discrete time fixed income options theory, we propose a stochastic programming procedure, which we call stochastic dedication, for managing asset/liability portfolios with interest rate contingent claims. The model uses scenario generation to combine deterministic dedication techniques with stochastic duration matching methods, and provides the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes. We employ a fixed income risk metric that can be interpreted as the fair market value of a collection of interest rate options that eliminates bankruptcy risk from the asset/liability portfolio. We incorporate this metric into a risk/return stochastic optimization model, using a binomial lattice sampling procedure to construct interest rate paths and cash flow streams from an arbitrage-free term structure model. The resulting parametric linear program has a particularly simple subproblem structure,...
99 citations
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TL;DR: This review explains the main concepts of stochastic dynamic programming and provides useful guidelines to implement this technique, including R code, using a wildlife management problem of the French wolf population.
Abstract: Summary
Under increasing environmental and financial constraints, ecologists are faced with making decisions about dynamic and uncertain biological systems. To do so, stochastic dynamic programming (SDP) is the most relevant tool for determining an optimal sequence of decisions over time.
Despite an increasing number of applications in ecology, SDP still suffers from a lack of widespread understanding. The required mathematical and programming knowledge as well as the absence of introductory material provide plausible explanations for this.
Here, we fill this gap by explaining the main concepts of SDP and providing useful guidelines to implement this technique, including R code.
We illustrate each step of SDP required to derive an optimal strategy using a wildlife management problem of the French wolf population.
Stochastic dynamic programming is a powerful technique to make decisions in presence of uncertainty about biological stochastic systems changing through time. We hope this review will provide an entry point into the technical literature about SDP and will improve its application in ecology.
99 citations
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TL;DR: Regular conditional versions of the forward and inverse Bayes formula are shown to have dual variational characterizations involving the minimization of apparent information and the maximization of compatible information, according to which Bayes' formula and its inverse are optimal information processors.
Abstract: We consider estimation problems, in which the estimand, X, and observation, Y, take values in measurable spaces. Regular conditional versions of the forward and inverse Bayes formula are shown to have dual variational characterizations involving the minimization of apparent information and the maximization of compatible information. These both have natural information-theoretic interpretations, according to which Bayes' formula and its inverse are optimal information processors. The variational characterization of the forward formula has the same form as that of Gibbs measures in statistical mechanics. The special case in which X and Y are diffusion processes governed by stochastic differential equations is examined in detail. The minimization of apparent information can then be formulated as a stochastic optimal control problem, with cost that is quadratic in both the control and observation fit. The dual problem can be formulated in terms of infinite-dimensional deterministic optimal control. Local versions of the variational characterizations are developed which quantify information flow in the estimators. In this context, the information conserving property of Bayesian estimators coincides with the Davis--Varaiya martingale stochastic dynamic programming principle.
99 citations
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TL;DR: This work proposes a new type of decomposition algorithm, based on the recently proposed framework of stochastic dual dynamic integer programming (SDDiP), to solve the multistage stochastics unit commitment (MSUC) problem and proposes a variety of computational enhancements to SDDiP.
Abstract: Unit commitment (UC) is a key operational problem in power systems for the optimal schedule of daily generation commitment. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning horizon is decided before the uncertainty is realized, or a multistage stochastic programming model with relatively small scenario trees to ensure tractability. We propose a new type of decomposition algorithm, based on the recently proposed framework of stochastic dual dynamic integer programming (SDDiP), to solve the multistage stochastic unit commitment (MSUC) problem. We propose a variety of computational enhancements to SDDiP, and conduct systematic and extensive computational experiments to demonstrate that the proposed method is able to handle elaborate stochastic processes and can solve MSUCs with a huge number of scenarios that are impossible to handle by existing methods.
99 citations
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TL;DR: The scenario generation (SG) algorithm proposed in this paper is a finite-element method that addresses this problem for the class of MSLP with random right-hand sides.
Abstract: A multistage stochastic linear program (MSLP) is a model of sequential stochastic optimization where the objective and constraints are linear. When any of the random variables used in the MSLP are continuous, the problem is infinite dimensional. To numerically tackle such a problem, we usually replace it with a finite-dimensional approximation. Even when all the random variables have finite support, the problem is often computationally intractable and must be approximated by a problem of smaller dimension. One of the primary challenges in the field of stochastic programming deals with discovering effective ways to evaluate the importance of scenarios and to use that information to trim the scenario tree in such a way that the solution to the smaller optimization problem is not much different from the problem stated with the original tree. The scenario generation (SG) algorithm proposed in this paper is a finite-element method that addresses this problem for the class of MSLP with random right-hand sides.
99 citations