2006, ISBN 0691119155, xii, 448

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance,...

Nonlinear theories | Mathematical optimization | MATHEMATICS | Applied | Mathematics

Nonlinear theories | Mathematical optimization | MATHEMATICS | Applied | Mathematics

Book

2003, Handbooks in operations research and management science, ISBN 0444508546, Volume 10, x, 688

Book

2002, Volume 128

Conference Proceeding

Mathematical Programming, ISSN 0025-5610, 10/2010, Volume 125, Issue 2, pp. 235 - 261

We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon...

Theoretical, Mathematical and Computational Physics | Nonsmooth Newton’s method | Secondary 91A25 | Mathematics | Value iteration | Policy iteration | Min-max Markov models | Mathematical Methods in Physics | 90C40 | 93E20 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Numerical Analysis | Combinatorics | Markov risk measures | 91B30 | Primary 49L20 | Nonsmooth Newton's method | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | CRITERION | STOCHASTIC-DOMINANCE | DISCRETE-TIME | UTILITY | Markov processes | Convergence (Social sciences) | Management science | Studies | Risk | Mathematical models | Markov analysis | Policies | Mathematical analysis | Horizon | Dynamic programming | Iterative methods | Convergence

Theoretical, Mathematical and Computational Physics | Nonsmooth Newton’s method | Secondary 91A25 | Mathematics | Value iteration | Policy iteration | Min-max Markov models | Mathematical Methods in Physics | 90C40 | 93E20 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Numerical Analysis | Combinatorics | Markov risk measures | 91B30 | Primary 49L20 | Nonsmooth Newton's method | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | CRITERION | STOCHASTIC-DOMINANCE | DISCRETE-TIME | UTILITY | Markov processes | Convergence (Social sciences) | Management science | Studies | Risk | Mathematical models | Markov analysis | Policies | Mathematical analysis | Horizon | Dynamic programming | Iterative methods | Convergence

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 2011, Volume 214, Issue 1, pp. 78 - 84

► Optimal order quantities depend on demand correlation. ► Optimal quantities can be approximated numerically. ► For very many products, the risk-neutral...

Risk analysis | Expected utility theory | Supply chain management | POLICY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRODUCTS | INVENTORY CONTROL | RESOURCE | Supply chain management Risk analysis Expected utility theory | Mathematical optimization | Analysis | Management science | Risk aversion | Studies | Utility functions | Approximations | Inventory management | Optimization algorithms | Expected utility | Demand | Utilities | Approximation | Mathematical analysis | Risk | Mathematical models | Optimization | Marketing

Risk analysis | Expected utility theory | Supply chain management | POLICY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRODUCTS | INVENTORY CONTROL | RESOURCE | Supply chain management Risk analysis Expected utility theory | Mathematical optimization | Analysis | Management science | Risk aversion | Studies | Utility functions | Approximations | Inventory management | Optimization algorithms | Expected utility | Demand | Utilities | Approximation | Mathematical analysis | Risk | Mathematical models | Optimization | Marketing

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 08/2006, Volume 31, Issue 3, pp. 433 - 452

We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of...

convex analysis | duality | stochastic optimization | risk measures | Risk aversion | Mathematical theorems | Optimal solutions | Topological theorems | Mathematical functions | Mathematical duality | Convexity | Topology | Banach space | Duality | Stochastic optimization | Convex analysis | Risk measures | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | COHERENT | STOCHASTIC-DOMINANCE | Usage | Duality theory (Mathematics) | Research | Convex programming | Stochastic processes | Analysis | Studies | Optimization algorithms | Risk | Stochastic models | Vector space

convex analysis | duality | stochastic optimization | risk measures | Risk aversion | Mathematical theorems | Optimal solutions | Topological theorems | Mathematical functions | Mathematical duality | Convexity | Topology | Banach space | Duality | Stochastic optimization | Convex analysis | Risk measures | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | COHERENT | STOCHASTIC-DOMINANCE | Usage | Duality theory (Mathematics) | Research | Convex programming | Stochastic processes | Analysis | Studies | Optimization algorithms | Risk | Stochastic models | Vector space

Journal Article

Operations Research, ISSN 0030-364X, 4/2011, Volume 59, Issue 2, pp. 346 - 364

We consider a multiproduct risk-averse newsvendor under the law-invariant coherent measures of risk. We first establish several fundamental properties of the...

risk aversion | coherent measures of risk | diversification | portfolio | multiple products | newsvendor | Risk aversion | Investment risk | Approximation | Optimal solutions | Utility functions | Coordinate systems | Mathematical vectors | Random variables | Financial portfolios | Order quantity | Multiple products | Newsvendor; risk aversion | Diversification | Coherent measures of risk | Portfolio | PORTFOLIO OPTIMIZATION | NEWSBOY PROBLEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | CONSTRAINTS | INVENTORY MODELS | CRITERION | STOCHASTIC-DOMINANCE | Investment analysis | Manufacturing processes | Research | Risk management | Analysis | Methods | Studies | Demand | Inventory control | Numerical analysis | Risk assessment

risk aversion | coherent measures of risk | diversification | portfolio | multiple products | newsvendor | Risk aversion | Investment risk | Approximation | Optimal solutions | Utility functions | Coordinate systems | Mathematical vectors | Random variables | Financial portfolios | Order quantity | Multiple products | Newsvendor; risk aversion | Diversification | Coherent measures of risk | Portfolio | PORTFOLIO OPTIMIZATION | NEWSBOY PROBLEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | CONSTRAINTS | INVENTORY MODELS | CRITERION | STOCHASTIC-DOMINANCE | Investment analysis | Manufacturing processes | Research | Risk management | Analysis | Methods | Studies | Demand | Inventory control | Numerical analysis | Risk assessment

Journal Article

9.
Full Text
Time-consistent approximations of risk-averse multistage stochastic optimization problems

Mathematical Programming, ISSN 0025-5610, 11/2015, Volume 153, Issue 2, pp. 459 - 493

In this paper we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We...

Time consistency | Theoretical, Mathematical and Computational Physics | Dynamic measures of risk | Mathematics | Decomposition | 90C15 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COHERENT | ACCEPTABILITY MEASURES | Management science | Algorithms | Studies | Optimization | Mathematical programming | Multistage | Approximation | Dynamics | Mathematical analysis | Coherence | Risk | Mathematical models | Stochasticity

Time consistency | Theoretical, Mathematical and Computational Physics | Dynamic measures of risk | Mathematics | Decomposition | 90C15 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COHERENT | ACCEPTABILITY MEASURES | Management science | Algorithms | Studies | Optimization | Mathematical programming | Multistage | Approximation | Dynamics | Mathematical analysis | Coherence | Risk | Mathematical models | Stochasticity

Journal Article

Operations Research, ISSN 0030-364X, 2/2011, Volume 59, Issue 1, pp. 125 - 132

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective...

two-stage models | risk | decomposition | stochastic programming | Risk aversion | Programming models | Financial risk | Decomposition methods | Linear programming | Mathematical vectors | Mathematical functions | Stochastic models | Modeling | Risk | Decomposition | Stochastic programming | Two-stage models | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DOMINANCE | MANAGEMENT | MIXED-INTEGER RECOURSE | Usage | Analysis | Decomposition (Mathematics) | Studies | Optimization techniques

two-stage models | risk | decomposition | stochastic programming | Risk aversion | Programming models | Financial risk | Decomposition methods | Linear programming | Mathematical vectors | Mathematical functions | Stochastic models | Modeling | Risk | Decomposition | Stochastic programming | Two-stage models | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DOMINANCE | MANAGEMENT | MIXED-INTEGER RECOURSE | Usage | Analysis | Decomposition (Mathematics) | Studies | Optimization techniques

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 10/2018, Volume 88, Issue 2, pp. 161 - 184

We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time...

Time consistency | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Operations Research/Decision Theory | Partially observable Markov processes | Mathematics | Dynamic programming | Business and Management, general | DECISION-PROCESSES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | SENSITIVE CONTROL | UNCERTAINTY | OPTIMIZATION | VARIANCE | STOCHASTIC-DOMINANCE | Measurement | Markov processes | Risk management | Discrete time systems

Time consistency | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Operations Research/Decision Theory | Partially observable Markov processes | Mathematics | Dynamic programming | Business and Management, general | DECISION-PROCESSES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | SENSITIVE CONTROL | UNCERTAINTY | OPTIMIZATION | VARIANCE | STOCHASTIC-DOMINANCE | Measurement | Markov processes | Risk management | Discrete time systems

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 08/2006, Volume 31, Issue 3, pp. 544 - 561

We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for...

dynamic programming | risk | multistage stochastic programming | conjugate duality | stochastic optimization | Risk aversion | Mathematical theorems | Algebra | Conditional probabilities | Axioms | Mathematical constants | Mathematical functions | Dynamic programming | Topological spaces | Risk | Conjugate duality | Multistage stochastic programming | Stochastic optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | COHERENT | STOCHASTIC-DOMINANCE | Research | Mappings (Mathematics) | Stochastic programming | Studies | Optimization techniques | Stochastic models | Risk assessment

dynamic programming | risk | multistage stochastic programming | conjugate duality | stochastic optimization | Risk aversion | Mathematical theorems | Algebra | Conditional probabilities | Axioms | Mathematical constants | Mathematical functions | Dynamic programming | Topological spaces | Risk | Conjugate duality | Multistage stochastic programming | Stochastic optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | COHERENT | STOCHASTIC-DOMINANCE | Research | Mappings (Mathematics) | Stochastic programming | Studies | Optimization techniques | Stochastic models | Risk assessment

Journal Article

1985, Springer series in computational mathematics, ISBN 3540127631, Volume 3, viii, 162

Book

Operations Research, ISSN 0030-364X, 11/2002, Volume 50, Issue 6, pp. 956 - 967

In a probabilistic set-covering problem the right-hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed...

Programming: integer | Programming: stochastic | Integers | Determinism | Optimal solutions | Algorithms | Probability distributions | Heuristics | Prunes | Mathematical vectors | Random variables | Children | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Fuzzy sets | Set theory | Research | Studies | Probability | Operations research | Mathematical models | Methods

Programming: integer | Programming: stochastic | Integers | Determinism | Optimal solutions | Algorithms | Probability distributions | Heuristics | Prunes | Mathematical vectors | Random variables | Children | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Fuzzy sets | Set theory | Research | Studies | Probability | Operations research | Mathematical models | Methods

Journal Article

Journal of Banking and Finance, ISSN 0378-4266, 2006, Volume 30, Issue 2, pp. 433 - 451

We consider the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution. We propose a new...

Portfolio optimization | Stochastic dominance | Risk | Duality | Utility function | Stochastic order | BUSINESS, FINANCE | portfolio optimization | MEAN-RISK MODELS | risk | utility function | ECONOMICS | duality | Stochastic analysis | Usage | Risk management | Portfolio management | Methods | Investment analysis | Analysis | Management science | Studies | Portfolio performance | Stochastic models | Rates of return | Optimization

Portfolio optimization | Stochastic dominance | Risk | Duality | Utility function | Stochastic order | BUSINESS, FINANCE | portfolio optimization | MEAN-RISK MODELS | risk | utility function | ECONOMICS | duality | Stochastic analysis | Usage | Risk management | Portfolio management | Methods | Investment analysis | Analysis | Management science | Studies | Portfolio performance | Stochastic models | Rates of return | Optimization

Journal Article

Mathematical Programming, ISSN 0025-5610, 12/2014, Volume 148, Issue 1, pp. 181 - 200

We propose a novel approach to quantification of risk preferences on the space of nondecreasing functions. When applied to law invariant risk preferences among...

Theoretical, Mathematical and Computational Physics | Mathematics | Conjugate duality | Kusuoka representation | Mathematical Methods in Physics | Quantile functions | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 91B16 | Numerical Analysis | 49N15 | Combinatorics | 46N10 | 91B30 | Risk measures | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | OPTIMIZATION | POINTS | UTILITY | Algebra | Computer science | Studies | Risk | Analysis | Mathematical programming | Conjugates | Quantiles | Mathematical analysis | Texts | Mathematical models | Representations | Random variables

Theoretical, Mathematical and Computational Physics | Mathematics | Conjugate duality | Kusuoka representation | Mathematical Methods in Physics | Quantile functions | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 91B16 | Numerical Analysis | 49N15 | Combinatorics | 46N10 | 91B30 | Risk measures | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | OPTIMIZATION | POINTS | UTILITY | Algebra | Computer science | Studies | Risk | Analysis | Mathematical programming | Conjugates | Quantiles | Mathematical analysis | Texts | Mathematical models | Representations | Random variables

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2009, Volume 117, Issue 1, pp. 111 - 127

We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector...

60E15 | Mathematical and Computational Physics | Stochastic order | Risk | Mathematics | Duality | 90C15 | 90C48 | Mathematical Methods in Physics | Utility | 90C46 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Optimality | Combinatorics | 46N10 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | optimality | utility | risk | stochastic order | duality | Studies | Lagrange multiplier | Optimization | Mathematical programming

60E15 | Mathematical and Computational Physics | Stochastic order | Risk | Mathematics | Duality | 90C15 | 90C48 | Mathematical Methods in Physics | Utility | 90C46 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Optimality | Combinatorics | 46N10 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | optimality | utility | risk | stochastic order | duality | Studies | Lagrange multiplier | Optimization | Mathematical programming

Journal Article

Operations Research, ISSN 0030-364X, 03/2007, Volume 55, Issue 2, pp. 378 - 394

We consider a supply chain operating in an uncertain environment: The customers demand is characterized by a discrete probability distribution. A...

multistage supply chain | scheduling | stochastic | inventory/production | integer | programming | transportation | Production efficiency | Supply chain management | Inventories | Algorithms | Probability distributions | Objective functions | Distribution costs | Trajectories | Raw materials | Shipments | Programming: integer | Inventory/production: multistage supply chain | Stochastic | Transportation: scheduling | SERVICE LEVEL CONSTRAINTS | APPROXIMATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Production planning | Mathematical optimization | Analysis | Integer programming | Studies | Optimization algorithms | Stochastic models | Supply chains

multistage supply chain | scheduling | stochastic | inventory/production | integer | programming | transportation | Production efficiency | Supply chain management | Inventories | Algorithms | Probability distributions | Objective functions | Distribution costs | Trajectories | Raw materials | Shipments | Programming: integer | Inventory/production: multistage supply chain | Stochastic | Transportation: scheduling | SERVICE LEVEL CONSTRAINTS | APPROXIMATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Production planning | Mathematical optimization | Analysis | Integer programming | Studies | Optimization algorithms | Stochastic models | Supply chains

Journal Article

Mathematical Programming, ISSN 0025-5610, 2018, pp. 1 - 28

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that...

Time consistency | Dynamic programming | Multistage stochastic programming | Dynamic risk measures | Mathematical analysis | Stochastic processes | Discrete time systems | Markov processes | Risk management | Portfolio management

Time consistency | Dynamic programming | Multistage stochastic programming | Dynamic risk measures | Mathematical analysis | Stochastic processes | Discrete time systems | Markov processes | Risk management | Portfolio management

Journal Article

Mathematical Programming, ISSN 0025-5610, 02/2019, pp. 1 - 21

We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We...

Risk | Representations | Disintegration | Mathematical programming

Risk | Representations | Disintegration | Mathematical programming

Journal Article

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