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Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes
Sladký, Karel
2020 - English
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.
Keywords:
Markov and semi-Markov reward processes; exponential utility function; risk sensitivity
Fulltext is available at external website.
Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes
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 ...
Macroeconomic Responses of Emerging Market Economies to Oil Price Shocks: Analysis by Region and Resource Profile
Togonidze, S.; Kočenda, Evžen
2020 - English
This study employs a vector autoregressive (VAR) model to analyse how oil price shocks affect macroeconomic fundamentals in emerging economies. Findings from existing literature remain inconclusive how macroeconomic variables fare towards shocks, especially in emerging economies. The objective of our study is to uncover if analysis by region (Latin America and the Caribbean, East Asia and the Pacific, Europe, and Central Asia) and resource intensity of economies (oil exporters, oil importers, minerals exporters, and less resource intensive). Our unique approach forms part of our contribution to the literature. We find that Latin America and the Caribbean are least affected by oil price shocks, while in East Asia and the Pacific the response of inflation and interest rate to oil price shocks is positive, and output growth is negative. Our analysis by resource endowment fails to show oil price shocks’ ability to explain huge variations in macroeconomic variables in oil importing economies. Further sensitivity analysis using US interest rates as an alternative source of external shocks to emerging economies establishes a significant response of interest rate responses to US interest rate in Europe and Central Asia, and in inflation in Latin America and the Caribbean. We also find that regardless of resource endowment, the response of output growth and capital to a positive US interest rate shock is negative and significant in EMs. Our results are persuasive that resource intensity and regional factors impact the responsiveness of emerging economies to oil price shocks, thus laying a basis for policy debate.\n
Keywords:
Emerging market economies; Oil price shocks; Output growth; Panel VAR
Fulltext is available at external website.
Macroeconomic Responses of Emerging Market Economies to Oil Price Shocks: Analysis by Region and Resource Profile
This study employs a vector autoregressive (VAR) model to analyse how oil price shocks affect macroeconomic fundamentals in emerging economies. Findings from existing literature remain inconclusive ...
Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making
Inuiguchi, M.; Jiroušek, Radim; Kratochvíl, Václav
2019 - English
The history of the series of the Czech-Japan seminars started in 1999. Thus, it is now more than 20 years ago when the first Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty was held in JAIST, Hokuriku. Since that time, these seminars were held in eleven splendid places in Japan, offering the Czech participants possibility to discover different parts of the Japanese islands. In reciprocity, it was the goal of the Czech partners organizing the past ten seminars to show the beauty of Czechia to Japanese colleagues, who, during the long Japan–Czech cooperation, became our close friends. This is also why the seminar has never visited one place two times.
Keywords:
Decision Making; Data Analysis; Uncertainty
Fulltext is available at external website.
Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making
The history of the series of the Czech-Japan seminars started in 1999. Thus, it is now more than 20 years ago when the first Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty ...
A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts
Daniel, M.; Kratochvíl, Václav
2019 - English
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In general, we make an effort to reach a simple upper bound function for $Conf$. (Nevertheless, the maximal value of conflict is, of course, equal to 1 for fully conflicting belief functions). We apply both theoretical research using the recent results on belief functions and also experimental computational approach here.
Keywords:
Belief functions; Dempster-Shafer theory; Uncertainty; Conflict-ing belief masses; Conflict between belief functions; Hidden conflict
Fulltext is available at external website.
A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In ...
Second Order Optimality in Markov and Semi-Markov Decision Processes
Sladký, Karel
2019 - English
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.
Keywords:
semi-Markov processes with rewards; discrete and continuous-time Markov reward chains; risk-sensitive optimality; average reward and variance over time
Fulltext is available at external website.
Second Order Optimality in Markov and Semi-Markov Decision Processes
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 ...
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates
Kaňková, Vlasta
2019 - English
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.
Keywords:
Two-objective stochastic optimization problems; scalarization; stochastic dominance; empirical estimates
Fulltext is available at external website.
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates
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 ...
Theory of SSB Representation of Preferences Revised
Pištěk, Miroslav
2019 - English
A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the classical (algebraic) case. Equipping a linear vector space with the so-called inductive linear topology, we derive the algebraic SSB representation on a topological basis, thus weakening\nthe convexity assumption. Such a unifying approach to SSB representation permits also to fully discuss the relationship of topological and algebraic axioms of continuity, and leads to a stronger existence result for a maximal element. By applying this theory to probability measures we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems in this context.
Keywords:
probability measures; inductive linear topology; topological vector space
Fulltext is available at external website.
Theory of SSB Representation of Preferences Revised
A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the ...
Preliminary Results from Experiments on the Behavior under Ambiguity
Jiroušek, Radim; Kratochvíl, Václav
2019 - English
In the literature, some experiments proving that human decision-makers manifest an ambiguity aversion are described. In our knowledge, no one has studied a possibility to measure the strength of this aversion and its stability in time. The research, we have recently started to realize should find out answers to these and similar questions. The goal of this paper is to present some preliminary results to initiate a discussion that should help us to modify either the process of data collection and/or the analysis of the collected data.
Keywords:
decision making; data analysis; measure
Fulltext is available at external website.
Preliminary Results from Experiments on the Behavior under Ambiguity
In the literature, some experiments proving that human decision-makers manifest an ambiguity aversion are described. In our knowledge, no one has studied a possibility to measure the strength of this ...
Algoritmický výběr dosažitelných preferencí
Siváková, Tereza; Kárný, Miroslav
2019 - Czech
Tato bakalářská práce se zabývá teorií optimálního rozhodování pro diskrétní markovský rozhodovací proces z hlediska volby preferencí. Za pomoci plně pravděpodobnostního návrhu, který zavádí tzv. ideální distribuci chování, která přiřazuje vysoké hodnoty pravděpodobnosti preferovanému chování a malé hodnoty pravděpodobnosti nežádoucímu chování, se hledá optimální rozhodovací politika. Tato práce obsahuje návod k nalezení optimální ideální distribuce chování a přináší obecnější řešení než řešení dosud známá. Dále přidává možnost respektování další preference, a to na volbu akcí. Vlastnosti výsledného rozhodování jsou ilustrovány simulačními experimenty. This bachelor’s thesis studies the optimal decision making for a discrete Markov decision process with a focus on preferences. By using a fully probabilistic design that introduces the so-called ideal behavior distribution, which has high probability values of preferred behaviors and small probability values of inappropriate behaviors, an optimal decision policy has been found. The thesis constructs an algorithm for selecting the optimal ideal behavior distribution and provides a more general solution than published ones. The thesis also opens a possibility to specify further preferences on selected actions. Properties of the resulting decision making are illustrated on simulated examples.
Keywords:
decision-making; probabilistic policies; quantification of aims
Fulltext is available at external website.
Algoritmický výběr dosažitelných preferencí
Tato bakalářská práce se zabývá teorií optimálního rozhodování pro diskrétní markovský rozhodovací proces z hlediska volby preferencí. Za pomoci plně pravděpodobnostního návrhu, který zavádí tzv. ...
Approximate Bayesian state estimation and output prediction using state-space model with uniform noise
Lainová, Eva; Kuklišová Pavelková, Lenka; Jirsa, Ladislav
2019 - English
This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and output prediction for states uniformly distributed on an orthotopic support and Bayesian filtering and output prediction for states uniformly distributed on a parallelotopic support are presented and compared.
Keywords:
Bayesian filtering; state estimation; output prediction; uniform noise; parallelotopic support; orthotopic support
Fulltext is available at external website.
Approximate Bayesian state estimation and output prediction using state-space model with uniform noise
This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and ...
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