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A Unified Framework for Risk-sensitive Markov Control Processes
Citation key Shen2014c
Author Shen, Y. and Stannat, W. and Obermayer, K.
Title of Book 53rd IEEE Conference on Decision and Control
Pages 1073-1078
Year 2014
ISSN 0191-2216
DOI 10.1109/CDC.2014.7039524
Abstract We introduce a unified framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate also unbounded costs, we study two types of infinite-horizon risk-sensitive criteria, discounted total risk and average risk, and solve the associated optimization problems by dynamic programming. For the discounted case, we propose a new discount scheme, which is different from the conventional form but consistent with the existing literature, while for the average risk criterion, we state Lyapunov-type stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation.
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