20240914 00:04 
Applicable Adaptive Discounted Fully Probabilistic Design of Decision Strategy
Molnárová, Soňa
The work addresses the issue of decreased utility of future rewards, referred to as discounting, while utilizing fully probabilistic design (FPD) of decision strategies. FPD obtains the optimal strategy for decision tasks using only probability distributions, which is its main asset. The standard way of solving decision tasks is provided by Markov decision processes (MDP), which FPD covers as a special case. Methods of solving discounted MDPs have already been introduced. However, the use of FPD might be advantageous when solving tasks with an unknown system model. Due to its probabilistic nature, FPD is able to obtain a more precise estimation of this model. After previously introducing discounting and system model estimation to FPD, the current work examines the effect of discounting on decision processes and its possible advantages when dealing with an unknown system model.
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20240324 00:07 
Central Moments and RiskSensitive Optimality in Markov Reward Processes
Sladký, Karel
In this note we consider discrete and continuoustime Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to select more sophisticated criteria that reflect also the variabilityrisk features of the problem. In this note we focus on models where the stream of rewards generated by the Markov process is evaluated by an exponential utility function with a given risk sensitivity coefficient (socalled risksensitive models).For the risk sensitive case, i.e. if the considered risksensitivity coefficient is nonzero, we establish explicit formulas for growth rate of expectation of the exponential utility function. Recall that in this case along with the total reward also it higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulas for calculating variance a higher central moments of the total reward generated by the Markov reward process along with its asymptotic behaviour.
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20240310 03:13 
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task\nand the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate. Regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values. Their recently proposed robust version turns out to be much more appropriate. Both\nillustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
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20240310 03:13 
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.
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20240310 03:13 
Some Robust Approaches to Reducing the Complexity of Economic Data
Kalina, Jan
The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given data. This paper starts with recalling the importance of Big Data in economics and with characterizing the main categories of dimension reduction techniques. While there have already been numerous techniques for dimensionality reduction available, this work is interested in methods that are robust to the presence of outlying measurements (outliers) in the economic data. Particularly, methods based on implicit weighting assigned to individual observations are developed in this paper. As the main contribution, this paper proposes three novel robust methods of dimension reduction. One method is a dimension reduction within a robust regularized linear regression, namely a sparse version of the least weighted squares estimator. The other two methods are robust versions of feature extraction methods popular in econometrics: robust principal component analysis and robust factor analysis.
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20240310 03:13 
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20240310 03:13 
Average Reward Optimality in SemiMarkov Decision Processes with Costly Interventions
Sladký, Karel
In this note we consider semiMarkov reward decision processes evolving on finite state spaces. We focus attention on average reward models, i.e. we establish explicit formulas for the growth rate of the total expected reward. In contrast to the standard models we assume that the decision maker can also change the running process by some (costly) intervention. Recall that the result for optimality criteria for the classical Markov decision chains in discrete and continuous time setting turn out to be a very specific case of the considered model. The aim is to formulate optimality conditions for semiMarkov models with interventions and present algorithmical procedures for finding optimal solutions.
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20231217 00:02 
Good vs. Bad Volatility in Major Cryptocurrencies: The Dichotomy and Drivers of Connectedness
Šíla, Jan ; Kočenda, Evžen ; Kukačka, Jiří ; Krištoufek, Ladislav
Cryptocurrencies exhibit unique statistical and dynamic properties compared to those of traditional financial assets, making the study of their volatility crucial for portfolio managers and traders. We investigate the volatility connectedness dynamics of a representative set of eight major crypto assets. Methodologically, we decompose the measured volatility into positive and negative components and employ the timevarying parameters vector autoregression (TVPVAR) framework to show distinct dynamics associated with market booms and downturns. The results suggest that crypto connectedness reflects important events and exhibits more variable and cyclical dynamics than those of traditional financial markets. Periods of extremely high or low connectedness are clearly linked to specific events in the crypto market and macroeconomic or monetary history. Furthermore, existing asymmetry from good and bad volatility indicates that information about market downturns spills over substantially faster than news about comparable market surges. Overall, the connectedness dynamics are predominantly driven by fundamental crypto factors, while the asymmetry measure also depends on macro factors such as the VIX index and the expected inflation.
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20231112 00:02 
On a stepladder model walking (with and without a decorator)
Polach, P. ; Prokýšek, R. ; Papáček, Štěpán
This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the realtime movement of the laboratory walking robot, designed and built at the Department of Control Theory of the Institute of Information Theory and Automation of the Czech Academy of Sciences [1, 6, 7]. Underactuated biped robots with an upper body form a subclass of legged robots, see, e.g., [4] for a review on the control of underactuated mechanical systems and [2] for a study of an asymptotically stable walking for biped robots. It is obvious that in general, the walking control of underactuated walking robots is a more challenging problem than walking control of fully actuated walking robots. As follows, we examine the wellknown mechanical system of the stepladder model with and without a decorator, whose role is substituted by an external inertial force according to the D’Alembert principle. It is well known, that stepladder walking is possible due to the periodic movement (pendulating) of an operator – decorator1 The rigorous dynamical analysis of stable cyclic walking of a class of stepladder models is presented in the next section.
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20230806 00:02 
Texture Spectral Similarity Criteria Comparison
Havlíček, Michal ; Haindl, Michal
Criteria capable of texture spectral similarity evaluation are presented and compared. From the fifteen evaluated criteria, only four criteria guarantee zero or minimal spectral ranking errors. Such criteria can support texture modeling algorithms by comparing the modeled texture with corresponding synthetic simulations. Another possible application is the development of texture retrieval, classification, or texture acquisition system. These criteria thoroughly test monotonicity and mutual correlation on specifically designed extensive monotonously degrading experiments.
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