Risksensitive Markov control processes
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, applying weighted norm spaces to incorporate also unbounded costs, we study two types of infinitehorizon risksensitive 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 Lyapunovlike stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.6317
 Bibcode:
 2011arXiv1110.6317S
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Mathematics  Dynamical Systems;
 Statistics  Machine Learning;
 60J05;
 93E20;
 93C55;
 47H07;
 91B06
 EPrint:
 21 pages