The average reward criterion is used to solve infinite-horizon MDPs. This risk-neutral criterion depends on the stochastic process in the limit and can use (i) the accumulated reward at infinity, which considers sequences of states of size \(h=\infty \) , or (ii) the steady state distribution of the MDP (i.e., the probability that the system is in each state in the long term), which considers sequences of states of size \(h=1\) . In many situations, it is desirable to consider risk during the process at each stage, which can be achieved with the average reward criterion using a utility function or a risk measure such as VaR and CVaR. The objective of this work is to propose a mathematical framework that allows a unified treatment of the existing literature using average reward and risk, including works that use exponential utility functions and CVaR, as well as to include interpretations with \(1 \le h \le \infty \) not present in the literature. These new interpretations allow differentiating policies that may not be distinguished from existing criteria. A numerical example shows the behaviors of the criteria considering this new framework.