Dynamic Stochastic Optimization

1. Front Matter

   Pages I-VIII

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2. Dynamic Decision Problems under Uncertainty: Modeling Aspects

   1. Front Matter

      Pages 1-1

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   2. Reflections on Output Analysis for Multistage Stochastic Linear Programs

      • Jitka Dupačová

      Pages 3-20

   3. Modeling Support for Multistage Recourse Problems

      • Peter Kall, János Mayer

      Pages 21-41

   4. Optimal Solutions for Undiscounted Variance Penalized Markov Decision Chains

      • Karel Sladký, Milan Sitař

      Pages 43-66

   5. Approximation and Optimization for Stochastic Networks

      • Julien Granger, Ananth Krishnamurthy, Stephen M. Robinson

      Pages 67-79

3. Dynamic Stochastic Optimization in Finance

   1. Front Matter

      Pages 81-81

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   2. Optimal Stopping Problem and Investment Models

      • Vadim I. Arkin, Alexander D. Slastnikov

      Pages 83-98

   3. Estimating LIBOR/Swaps Spot-Volatilities: the EpiVolatility Model

      • Stephen W. Bianchi, Roger J-B Wets, Liming Yang

      Pages 99-114

   4. Structured Products for Pension Funds

      • M. A. H. Dempster, M. Germano, E. A. Medova, M. Villaverde

      Pages 115-130

4. Optimal Control Under Stochastic Uncertainty

   1. Front Matter

      Pages 131-131

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   2. Real-time Robust Optimal Trajectory Planning of Industrial Robots

      • Andreas Aurnhammer, Kurt Marti

      Pages 133-154

   3. Adaptive Optimal Stochastic Trajectory Planning and Control (AOSTPC) for Robots

      • K. Marti

      Pages 155-206

5. Tools for Dynamic Stochastic Optimization

   1. Front Matter

      Pages 207-207

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   2. Solving Stochastic Programming Problems by Successive Regression Approximations — Numerical Results

      • István Deák

      Pages 209-224

   3. Stochastic Optimization of Risk Functions via Parametric Smoothing

      • Yuri Ermoliev, Vladimir Norkin

      Pages 225-247

   4. Optimization under Uncertainty using Momentum

      • Sjur Didrik Flåm

      Pages 249-256

   5. Perturbation Analysis of Chance-constrained Programs under Variation of all Constraint Data

      • René Henrion

      Pages 257-274

   6. The Value of Perfect Information as a Risk Measure

      • Georg Ch. Pflug

      Pages 275-291

   7. New Bounds and Approximations for the Probability Distribution of the Length of the Critical Path

      • András Prékopa, Jianmin Long, Tamás Szántai

      Pages 293-320

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in­ that may have a nonsmooth and even discontinuous character - the tegrands typical situation for "hit-or-miss" type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations.

• Analysis
• Stochastic Decision Processes
• Stochastic Networks
• Stochastic Optimization
• Stochastic Programming
• optimal control
• optimization

• Aero-Space Engineering and Technology, Federal Armed Forces University Munich, Neubiberg/Munich, Germany

  Kurt Marti

• IIASA Laxenburg, Laxenburg/Wien, Austria

  Yuri Ermoliev

• Institute of Statistics and Decision Support Systems (ISDS), University of Wien, Wien, Austria

  Georg Pflug

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