Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates

2018/03/26 by Guo, Xin, Liu, Qiuli, Zhang, Yi
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1803.09580

Abstract

We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the existence and uniqueness of the solution to the optimality equation out of a class of possibly unbounded functions, to which the Feynman-Kac formula was also justified to hold.

Related

• Continuous-time Markov decision processes under the risk-sensitive average cost criterion
• Continuous-time Markov decision processes with exponential utility
• Continuous-time Markov Decision Processes with Finite-horizon Expected Total Cost Criteria
• On risk-sensitive piecewise deterministic Markov decision processes
• Risk-sensitive control of continuous time Markov chains