|
|
Empirical Estimates in Stochastic Optimization: Special cases
Kaňková, Vlasta
Classical optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are relatively complicated. On the other hand, these problems fulfil very often "suitable" mathematical properties guaranteing the stability (w.r.t. probability measure) and, moreover, giving a possibility to replace the "underlying" probability measure by an empirical one to obtain "good" stochastic estimates of the optimal value and the optimal solution. Properties of thess estimates have been investigated mostly for standard types of probability measures with suitable (thin) tails and independent random samples. However distributions with heavy tails correspond to many economic problems and, moreover, many applications do not correspond to the "classical" problems. The aim of the paper is, first, to try to recall stability results including also heavy tails and more general problems.
|
|
| |
|
|
Pravděpodobnostní vlastnosti spojité dvojité aukce - rovnoměrný případ
Šmíd, Martin
We study probabilistic properties of a zero intelligence model of a limit order market, very similar to those of /citet{Maslov00} and /citet{Smith03}. We (recursively) describe the distributions of the order books and the best quotes. Based on these theoretical results, a procedure for statistical inference of the model may be designed and the evolution of the process may be simulated more efficiently then by the crude simulation of all the events.
|
|
| |
|
|
Poznámka k empirickým odhadům v ekonomických úlohách
Kaňková, Vlasta
Optimization problems depending on a probability measure correspond to many economic applications. Since the ``underlying" measure is usually unknown the decision is mostly determined on the data basis, it means on statistical (mostly empirical) estimates of the probability measure. Properties of the optimal value (and solution) estimates have been investigated many times. There were introduced assumptions under which the asymptotic distribution is normal and the convergence rate is at least exponential. We generalize the assertions concerning rate convergence. Especially we shall consider distribiotions with the Pareto tails. The introduced assertions are focus on optimal value estimates.
|
|
|
Problém dvou manažérů a problematika úloh stochastického programování s lineární kompenzací
Kaňková, Vlasta
Stochastic programming problems with linear recourse correspond to many economic problems. It is generally known that these problems are a composition of two (outer and inner) optimization problems. A solution of the outer problem depends on an ``underlying" probability measure while a solution of the inner problem depends on the solution of the outer problem and on the random element realization. Evidently, a position and optimal behaviour of two managers can be (in many cases) described by this type of the model in which the optimal behaviour of the main manager is determined by the outer problem while the optimal behaviour of the second manager is described by the inner problem. We focus on an investigation of properties of the inner problem.
|
|
|
Model pro rozdíl dvou Poissonových veličin
Volf, Petr
When the discrete count data are analyzed, we are often facing the problems with insufficient flexibility of Poisson distribution. However, in many instances the variable of the interest is the difference of two count variables. For these cases, so called Skellam distribution is available, derived originally as the difference of two correlated Poissons. The model contains latent variables, which leads quite naturally to the use of Bayes approach and to data augmentation via the Markov Chain Monte Carlo generation.
|
|
|
Vícekriteriální úlohy stochastického programování a vícesrupňové úlohy
Kaňková, Vlasta
Economic activities developing over time are very often influenced simultaneously by a random factor (modelled mostly by a stochastic process)and a decission parameter that has to be chosen according to economic possibilities. Moreover, it is necessary often to evaluate the economic activities simultaneously by a few ``utility" functions. Evidently, the mentioned economic situations can lead to mathematical models corresponding to multistage multiobjective stochastic programming problems. Usually, the multiobjective (one-stage) problems and multistage (one-objective) problems have been investigated separately. The aim of the contribution will be to try to analyze a relationship berween rhese two approaches.
|
|
| |
|
|
Empirické odhady a stabilita ve stochastickém programování
Kaňková, Vlasta
It is known that optimization problems depending on a probability measure correspond to many applications. It is also known that these problems belong mostly to a class of nonlinear optimization problems and, moreover, that very often an ``underlying" probability measure is not completely known. The aim of the research report is to deal with the case when an empirical measure substitutes the theoretical one. In particular, the aim is to generalize reults dealing with convergence rate in the case of empirical esrimates. The introduced results are based on the stability results corresponding to the Wasserstein metric. A relationship berween tails of one-dimensional marginal distribution functions and exponentional rate of convergence are introduced. The corresponding results are focus mainly on ``classical" type of problems corresponding to the cases with penalty and recourse. However, an integer simple recourse case and some special risk funkcionals are discussed also.
|
guest ::
