Národní úložiště šedé literatury Nalezeno 12 záznamů.  1 - 10další  přejít na záznam: Hledání trvalo 0.01 vteřin. 
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric
Kaňková, Vlasta
Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved on the data base. Point estimates of an optimal value and estimates of an optimal solutionset can be obtained by this approach. A consistency, a rate of convergence and normal properties, of these estimates, have been discussed (many times) not only under assumptions of independent data corresponding to the distributions with light tails, but also for weak dependent data and the distributions with heavy tails. However, it is also possible to estimate (on the data base) a confidence intervals and bounds for the optimal value and the optimal solutions. To analyze this approach we focus on a special case of static problems depending nonlineary on the probability measure. Stability results based on the Wasserstein metric and the Valander approach will be employed for the above mentioned analysis.
Analysis of Impact of Covariates Entering Stochastic Optimization Problem
Volf, Petr
In the contribution we study consequences of imperfect information to precision of stochastic optimization solution. In particular, it is assumed that the characteristics of optimization problem are influenced by a set of covariates. This dependence is described via a regression model. Hence, the uncertainty is then caused by statistical estimation of regression parameters. The contribution will analyze several regression model cases, together with their application. Precision of results will be explored, both theoretically as well as with the aid of simulations.
Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes
Sladký, Karel
This contribution is devoted to risk-sensitivity in long-run average optimality of Markov and semi-Markov reward processes. Since the traditional average optimality criteria cannot reflect the variability-risk features of the problem, we are interested in more sophisticated approaches where the stream of rewards generated by the Markov chain that is evaluated by an exponential utility function with a given risk sensitivity coefficient. Recall that for the risk sensitivity coefficient equal to zero (i.e. the so called risk-neutral case) we arrive at traditional optimality criteria, if the risk sensitivity coefficient is close to zero the Taylor expansion enables to evaluate variability of the generated total reward. Observe that the first moment of the total reward corresponds to expectation of total reward and the second central moment to the reward variance. In this note we present necessary and sufficient risk-sensitivity and risk-neutral optimality conditions for long run risk-sensitive average optimality criterion of unichain Markov and semi-Markov reward processes.
A Note on Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure
Kaňková, Vlasta
Nonlinear dependence on a probability measure begins to appear (last time) in a stochastic optimization rather often. Namely, the corresponding type of problems corresponds to many situations in applications. The nonlinear dependence can appear as in the objective functions so in a constraints set. We plan to consider the case of static (one-objective) problems in which nonlinear dependence appears in the objective function with a few types of constraints sets. In details we consider constraints sets “deterministic”, depending nonlinearly on the probability measure, constraints set determined by second order stochastic dominance and the sets given by mean-risk problems. The last case means that the constraints set corresponds to solutions those guarantee an acceptable value in both criteria. To introduce corresponding assertions we employ the stability results based on the Wasserstein metric and L1 norm. Moreover, we try to deal also with the case when all results have to be obtained (estimated) on the data base.
Use of the BCC and Range Directional DEA Models within an Efficiency Evaluation
Houda, Michal
The contribution deals with two data envelopment analysis (DEA) models, in particular the BCC model (radial DEA model with variable returns to scale), and the range directional model. The mathematical description of the models are provided and several properties reported. A numerical comparison of the two models on real industrial data is provided with discussion about possible drawbacks of simplifying modeling procedures.
Bivariate Geometric Distribution and Competing Risks: Statistical Analysis and Application
Volf, Petr
The contribution studies the statistical model for discrete time two-variate duration (time-to-event) data. The analysis is complicated by partial data observation caused either by the right-side censoring or by the presence of dependent competing events. The case is modeled and analyzed with the aid of a two-variate geometric distribution. The model identifiability is discussed and it is shown that the model is not identifiable without proper additional assumptions. The method of analysis is illustrated both on artificially generated\nexample and on real unemployment data.
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates
Kaňková, Vlasta
Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model depending on a probability measure. We focus on a special case of one-stage two objective stochastic “Mean-Risk problem”. Of course to determine optimal solution simultaneously with respect to the both criteria is mostly impossible. Consequently, it is necessary to employ some approaches. A few of them are known (from the literature), however two of them are very important: first of them is based on a scalarizing technique and the second one is based on the stochastic dominance. First approach has been suggested (in special case) by Markowitz, the second approach is based on the second order stochastic dominance. The last approach corresponds (under some assumptions) to partial order in the set of the utility functions.\nThe aim of the contribution is to deal with the both main above mentioned approaches. First, we repeat their properties and further we try to suggest possibility to improve the both values simultaneously with respect to the both criteria. However, we focus mainly on the case when probability characteristics has to be estimated on the data base.
Second Order Optimality in Markov and Semi-Markov Decision Processes
Sladký, Karel
Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per time may be quite insufficient to characterize the problem from the point of a decision maker. To this end it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean-variance selection rules, i.e. we optimize the weighted sum of average or total reward and its variance. Such approach has been already studied for very special classes of semi-Markov decision processes, in particular, for Markov decision processes in discrete - and continuous-time setting. In this note these approaches are summarized and possible extensions to the wider class of semi-Markov decision processes is discussed. Attention is mostly restricted to uncontrolled models in which the chain is aperiodic and contains a single class of recurrent states. Considering finite time horizons, explicit formulas for the first and second moments of total reward as well as for the corresponding variance are produced.
Application of the Cox regression model with time dependent parameters to unemployment data
Volf, Petr
The contribution deals with the application of statistical survival analysis with the intensity described by a generalized version of Cox regression model with time dependent parameters. A\nmethod of model components non-parametric estimation is recalled, the flexibility of result is assessed with a goodness-of-fit test based on martingale residuals. The application\nconcerns to the real data representing the job opportunities development and reduction, during a given period. The risk of leaving the company is changing in time and depends also on the age of employees and their time with company. Both these covariates are considered and their impact to the risk analyzed.
Multi-Objective Optimization Problems with Random Elements - Survey of Approaches
Kaňková, Vlasta
Many economic and financial situations depend simultaneously on a random element and a decision parameter. Mostly, it is possible to influence the above mentioned situation only by an optimization model depending on a probability measure. This optimization problem can be static (one-stage), dynamic with finite or infinite horizon, single-objective or multi-objective. We focus on one-stage multi-objective problems corresponding to applications those are suitable to evaluate simultaneously by a few objectives. The aim of the contribution is to give a survey of different approaches (as they are known from the literature) of the above mentioned applications. To this end we start with well-known mean-risk model and continue with other known approaches. Moreover, we try to complete every model by a suitable application. Except an analysis of a choice of the objective functions type we try to discuss suitable constraints set with respect to the problem base, possible investigation and relaxation. At the end we mention properties of the problem in the case when the theoretical „underlying“ probability measure is replaced by its „deterministic“ or „stochastic“ estimate.

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