Controlled Markov chains with exponential risk-sensitive criteria: modularity, structured policies and applications

This work concerns controlled Markov chains models with a countable state space, under (exponential) total and discounted risk-sensitive cost criteria. A set of general conditions is presented to obtain structural properties of the optimal value function and policies. In particular, monotonicity properties of value functions and optimal policies are established. Three applications studies are used to illustrate the general results obtained in the paper: equipment replacement, optimal resource allocation, and inventory control.