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Risk-sensitive Markov Control Processes
Citation key Shen2013
Author Shen, Y. and Stannat, W. and Obermayer, K.
Pages 3652–3672
Year 2013
DOI 10.1137/120899005
Journal SIAM Journal on Control and Optimization
Volume 51
Number 5
Abstract We introduce a general 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, apply- ing weighted norm spaces to incorporate unbounded costs also, 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-like stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation.
Bibtex Type of Publication Selected:main selected:reinforcement selected:decision selected:publications
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