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Optimal Value of Loans via Stochastic Programming
Kaňková, Vlasta
A question of mortgage leads to serious and complicated problems of financial mathematics. On one side is a bank with an aim to have a “good” profit, on the other side is the client trying to invest money safely, with possible “small” risk.Let us suppose that a young married couple is in a position of client. Young people know that an expected and also unexpected unpleasant financial situation can happen. Many unpleasant financial situation can be caused by a random factor. Consequently stochastic methods are suitable to secure against them. The aim of the suggested model is not only to state a maximal reasonable value of loans, but also to endure unpleasant financial period. To this end we employ stochastic optimization theory. A few suitable models will be introduced. The choice of the model depends on environment of the young people. Models will be with “deterministic” constraints, probability constraints, but also with stochastic dominance constraints. The suggested models will be analyzed both from the numerical point of view and from possible method solution based on data. Except static one-objective problem we suggest also multi–objective models.
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Avoiding overfitting of models: an application to research data on the Internet videos
Jiroušek, Radim ; Krejčová, I.
The problem of overfitting is studied from the perspective of information theory. In this context, data-based model learning can be viewed as a transformation process, a process transforming the information contained in data into the information represented by a model. The overfitting of a model often occurs when one considers an unnecessarily complex model, which usually means that the considered model contains more information than the original data. Thus, using one of the basic laws of information theory saying that any transformation cannot increase the amount of information, we get the basic restriction laid on models constructed from data: A model is acceptable if it does not contain more information than the input data file.
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Risk-Sensitive Optimality in Markov Games
Sladký, Karel ; Martínez Cortés, V. M.
The article is devoted to risk-sensitive optimality in Markov games. Attention is focused on Markov games evolving on communicating Markov chains with two-players with opposite aims. Considering risk-sensitive optimality criteria means that total reward generated by the game is evaluated by exponential utility function with a given risk-sensitive coefficient. In particular, the first player (resp. the secondplayer) tries to maximize (resp. minimize) the long-run risk sensitive average reward. Observe that if the second player is dummy, the problem is reduced to finding optimal policy of the Markov decision chain with the risk-sensitive optimality. Recall that for the risk sensitivity coefficient equal to zero we arrive at traditional optimality criteria. In this article, connections between risk-sensitive and risk-neutral Markov decisionchains and Markov games models are studied using discrepancy functions. Explicit formulae for bounds on the risk-sensitive average long-run reward are reported. Policy iteration algorithm for finding suboptimal policies of both players is suggested. The obtained results are illustrated on numerical example.
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Robust Regression Estimators: A Comparison of Prediction Performance
Kalina, Jan ; Peštová, Barbora
Regression represents an important methodology for solving numerous tasks of applied econometrics. This paper is devoted to robust estimators of parameters of a linear regression model, which are preferable whenever the data contain or are believed to contain outlying measurements (outliers). While various robust regression estimators are nowadays available in standard statistical packages, the question remains how to choose the most suitable regression method for a particular data set. This paper aims at comparing various regression methods on various data sets. First, the prediction performance of common robust regression estimators are compared on a set of 24 real data sets from public repositories. Further, the results are used as input for a metalearning study over 9 selected features of individual data sets. On the whole, the least trimmed squares turns out to be superior to the least squares or M-estimators in the majority of the data sets, while the process of metalearning does not succeed in a reliable prediction of the most suitable estimator for a given data set.
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