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  • HU Berlin  (238)
  • Anna-Ditzen-Bibliothek Neuenhagen
  • Technikmuseum Berlin
  • Higle, Julie L.  (238)
  • Open access  (238)
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  • HU Berlin  (238)
  • Anna-Ditzen-Bibliothek Neuenhagen
  • Technikmuseum Berlin
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  • Open access  (238)
  • 1
    Online Resource
    Online Resource
    Stochastic programming by Monte Carlo simulation methods (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8878
    Format: 1 Online-Ressource (30 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,3
    Content: We consider in this paper stochastic programming problems which can be formulated as an optimization problem of an expected value function subject to deterministic constraints. We discuss a Monte Carlo simulation approach based on sample average approximations to a numerical solution of such problems. In particular, we give a survey of a statistical inference of the sample average estimators of the optimal value and optimal solutions of the true problem. We also discuss stopping rules and a validation analysis for such sample average approximation optimization procedures and give some illustration examples.
    Language: English
    DOI: 10.18452/8226
    URN: urn:nbn:de:kobv:11-10046191
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    HU Berlin
  • 2
    Online Resource
    Online Resource
    Variable-sample methods and simulated annealing for discrete stochastic optimization : (revised version) (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8879
    Format: 1 Online-Ressource (36 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,4
    Content: In this paper we study a modifcation of the well-known simulated annealing method, adapting it to discrete stochastic optimization problems. Our algorithm is based on a variable-sample Monte Carlo technique, in which the objective function is replaced, at each iteration, by a sample average approximation. The idea is to obtain independent estimates of the objective function, to avoid getting "trapped" in a single sample-path. We first provide general results under which variable-sample methods yield consistent estimators as well as bounds on the estimation error. Then, we concentrate on the simulated annealing algorithm, and derive a proper schedule of sample sizes that guarantees convergence of the overall algorithm w.p.1. Because the convergence analysis is done sample-path wise (by means of the law of the iterated logarithm), we are able to obtain our results in a exible setting, which includes the possibility of using different neighborhood structures and different sampling distributions along the algorithm, without making strong assumptions on the underlying distributions.
    Language: English
    DOI: 10.18452/8227
    URN: urn:nbn:de:kobv:11-10046200
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    HU Berlin
  • 3
    Online Resource
    Online Resource
    The performance of stochastic dynamic and fixed mix portfolio models (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8885
    Series Statement: Stochastic Programming E-Print Series 2000,2000,9
    Content: The purpose of this paper is to demonstrate how to evaluate stochastic programming models, and more specifically to compare two different approaches to asset liability management. The first uses multistage stochastic programming, while the other is a static approach based on so-called constant rebalancing of fixed mix. Particular attention is paid to the methodology used for the comparison. The two alternatives are tested over a large number of realistic scenarios created by means of simulation. We find that due to the ability of the stochastic programming model to adapt to the information in the scenario tree, it dominates the fixed mix approach.
    Language: English
    DOI: 10.18452/8233
    URN: urn:nbn:de:kobv:11-110-18452/8885-3
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    HU Berlin
  • 4
    Online Resource
    Online Resource
    The Application of Operations Research Techniques to Financial Markets (1999)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8874
    Format: 1 Online-Ressource (32 Seiten)
    Series Statement: Stochastic Programming E-Print Series 1999,1999,6
    Content: This paper reviews the application of OR to financial markets. After considering reasons for the attractiveness of general finance problems to OR researchers, the main types of financial market problem amendable to OR are identified, and some of the many problems solved using OR are documented. While mathematical programming is the most widely applied technique, Monte Carlo and other simulation methods are increasingly widely used. OR now plays an important role in the operation of financial markets and this importance is likely to increase, creating the opportunity for OR (and operation researchers) to play an even greater role.
    Language: English
    DOI: 10.18452/8222
    URN: urn:nbn:de:kobv:11-10057384
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    HU Berlin
  • 5
    Online Resource
    Online Resource
    Scenario reduction in stochastic programming: An approach using probability metrics (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8896
    Series Statement: Stochastic Programming E-Print Series 2000,2000,20
    Content: Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after a 50% reduction of the scenario tree the optimal reduced tree still has about 90% of relative accuracy.
    Language: English
    DOI: 10.18452/8244
    URN: urn:nbn:de:kobv:11-110-18452/8896-9
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    HU Berlin
  • 6
    Online Resource
    Online Resource
    Mean-variance versus expected utility in dynamic investment analysis (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8890
    Format: 1 Online-Ressource (29 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,14
    Content: This paper derives the mean-variance efficient frontier and optimal portfolio policies for a dynamic investment model. In the absence of arbitrage opportunities, the optimal expected portfolio value can be identified through the state price density in a frictionless market using martingale analysis. The efficient frontier for the dynamic model is linear in the space of the standard deviation and the expected value of the terminal portfolio in the presence of a riskless asset as in the static mean-variance case. A replication procedure is developed to obtain the optimal portfolio policies using a partial differential equation. A closed form solution is derived if asset prices jointly follow a multidimensional geometric Brownian motion. A comparison is made between the optimal policies of the expected utility approach and a mean-variance analysis in the continuous time setting. For investors interested in the mean-variance criterion, we discuss and derive the optimal choice of target wealth that maximizes the probability that the mean-variance analysis outperforms the expected utility approach.
    Language: English
    DOI: 10.18452/8238
    URN: urn:nbn:de:kobv:11-10057675
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    HU Berlin
  • 7
    Online Resource
    Online Resource
    Robust path choice in networks with failures (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8884
    Series Statement: Stochastic Programming E-Print Series 2000,2000,8
    Content: The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur according to a continuous-time Markov chain. The objective is to develop a routing strategy that minimizes the total expected travel time. Dynamic programming models and flow-oriented models are developed and analyzed in the uncapacitated and the capacitated case. It is shown that the robust plan can be found from a special two-stage stochastic programming problem in which the second stage models the re-routing problem after the state transition in the network. The models are illustrated on an example of the Sioux Falls transportation network.The computational results reveal striking properties of different routing policies and show that substantial improvements in both duration and size of jams can be achieved by employing robust strategies.
    Language: English
    DOI: 10.18452/8232
    URN: urn:nbn:de:kobv:11-110-18452/8884-8
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    HU Berlin
  • 8
    Online Resource
    Online Resource
    Dual stochastic dominance and related mean-risk models (2001)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8905
    Series Statement: Stochastic Programming E-Print Series 2001,2001,2
    Content: We consider the problem of constructing mean-risk models which are consistent with the second degree stochastic dominance relation. By exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions. This allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation. We also provide stochastic linear programming formulations of these models.
    Language: English
    DOI: 10.18452/8253
    URN: urn:nbn:de:kobv:11-110-18452/8905-8
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    HU Berlin
  • 9
    Online Resource
    Online Resource
    Applying the minimum risk criterion in stochastic recourse programs (2001)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8911
    Series Statement: Stochastic Programming E-Print Series 2001,2001,8
    Content: In the setting of stochastic recourse programs, we consider the problem of minimizing the probability of total costs exceeding a certain threshold value. The problem is referred to as the minimum risk problem and is posed in order to obtain a more adequate description of risk aversion than that of the accustomed expected value problem. We establish continuity properties of the recourse function as a function of the first-stage decision, as well as of the underlying probability distribution or random parameters. This leads to stability results for the optimal solution of the minimum risk problem when the underlying probability distribution is subjected to perturbations. Furthermore, an algorithm for the minimum risk problem is elaborated and we present results of some preliminary computational experiments.
    Language: English
    DOI: 10.18452/8259
    URN: urn:nbn:de:kobv:11-110-18452/8911-0
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    HU Berlin
  • 10
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    Online Resource
    Stochastic programming duality : L ∞ multipliers with an application to mathematical finance (2001)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8912
    Format: 1 Online-Ressource (22 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2001,2001,9
    Content: A new duality theory is developed for a class of stochastic programs in which the probability distribution is not necessarily discrete. This provides a new framework for problems which are not necessarily bounded, are not required to have relatively complete recourse, and do not satisfy the typical Slater condition of strict feasibility. These problems instead satisfy a different constraint qualification called "direction-free feasibility" to deal with possibly unbounded constaint sets, and "calmness" of a certain finite-dimensional value function to serve as a weaker condition than strict feasibility to obtain the existence of dual mulitpliers. In this way, strong duality results are established in which the dual variables are finite-dimensional, despite the possible intinite-dimensional character of the second-stage constraints. From this, infinite-dimensional dual problems are obtained in the space of essentially bounded functions. It is then shown how this framework could be used to ontain duality result in the setting of mathematical finance.
    Language: English
    DOI: 10.18452/8260
    URN: urn:nbn:de:kobv:11-10058217
    URN: urn:nbn:de:kobv:11-10058226
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    HU Berlin
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