TY - GEN
T1 - Risk-averse control of continuous-time markov chains
AU - Dentcheva, Darinka
AU - Ruszczynski, Andrzej
N1 - Publisher Copyright:
Copyright © by SIAM.
PY - 2017
Y1 - 2017
N2 - We develop an approach to time-consistent risk control of continuous-time processes in Markov systems with finite state space. Our analysis is based on time-consistent risk evaluation in continuous time, which uses the dual representation of dynamic coherent risk measures. Introducing a suitable differentiability concept for multivalued mappings and a concept of strong time consistency, we approximate the risk multikernels of the Markov system via set-valued derivatives, which gives rise to the concept of a risk multigenerator of a Markov process. We focus on risk-averse Markov decision problems with cost evaluated at the terminal state. We derive a system of ordinary differential equations for the risk evaluation of a given policy, which generalize the classical backward Kolmogorov equations for Markov processes. Furthermore, we establish optimality conditions in form of differential equation involving the support function of the risk multigenerator and we identify conditions for the existence of an optimal Markov policy.
AB - We develop an approach to time-consistent risk control of continuous-time processes in Markov systems with finite state space. Our analysis is based on time-consistent risk evaluation in continuous time, which uses the dual representation of dynamic coherent risk measures. Introducing a suitable differentiability concept for multivalued mappings and a concept of strong time consistency, we approximate the risk multikernels of the Markov system via set-valued derivatives, which gives rise to the concept of a risk multigenerator of a Markov process. We focus on risk-averse Markov decision problems with cost evaluated at the terminal state. We derive a system of ordinary differential equations for the risk evaluation of a given policy, which generalize the classical backward Kolmogorov equations for Markov processes. Furthermore, we establish optimality conditions in form of differential equation involving the support function of the risk multigenerator and we identify conditions for the existence of an optimal Markov policy.
UR - http://www.scopus.com/inward/record.url?scp=85029435609&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029435609&partnerID=8YFLogxK
U2 - 10.1137/1.9781611975024.11
DO - 10.1137/1.9781611975024.11
M3 - Conference contribution
AN - SCOPUS:85029435609
T3 - Proceedings of the SIAM Conference on Control and Its Applications, CT 2017
SP - 78
EP - 85
BT - Proceedings of the SIAM Conference on Control and Its Applications, CT 2017
A2 - Kang, Wei
A2 - Barbot, Jean-Pierre
A2 - Zhang, Qing
A2 - Liu, Ruihua
T2 - 2017 SIAM Conference on Control and Its Applications, CT 2017
Y2 - 10 July 2017 through 12 July 2017
ER -