National Repository of Grey Literature 3 records found  Search took 0.01 seconds. 
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains
Sladký, Karel
In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.
Optimalita za rizika a typu střední hodnota - rozptyl v markovskýách rozhodovacích procesech
Sladký, Karel ; Sitař, Milan
In this note, we compare two aproaches for handling risk-variability features arising in discrete-time Markov decision processes: models with exponential utility function and mean variance optimality models. Computational approaches for finding optimal decision with respect to the optimality criteria mentioned above are presented and analytical results showing connections between the above optimality criteria are discussed.
Techniques and instruments of decision making under risk for one-phase decision problems.
Horčička, Jan ; Švecová, Lenka (advisor) ; Fotr, Jiří (referee)
This thesis is focused on decision models for decision making under risk and uncertainty. The thesis should give a comprehensive insight about individual decision criteria and the reader should form a clear picture about usability of these models for solving particular decision problems. The thesis tries to provide objective point of view to the reader with highlighting the advantages and disadvantages of each model. In the frame of decision making under risk, the thesis mentions the expected value rule, the rule of expected value and variance and the stochastic dominance rules. For the field of decision making under uncertainty, the thesis brings up the Laplace's criterion, the Hurwicz's criterion and Savage's regret criterion. The thesis further deal with the theory of expected utility. It brings up the method of construction of the utility curve, methods of usage and also known deficiencies of the theory when used in real world situations. In connection with utility theory, the thesis introduces the expected utility rule. For mapping future development, the thesis work with probability trees and explains their usability for modeling situations under risk and uncertainty. For all of the featured decision criteria, the work shows their applicative usage by using a prefigurative example. The reader should therefore know, how to proceed when using mentioned models for solving real decision problems.

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