  We consider the stochastic shortest path planning problem in MDPs, i.e., the
problem of designing policies that ensure reaching a goal state from a given
initial state with minimum accrued cost. In order to account for rare but
important realizations of the system, we consider a nested dynamic coherent
risk total cost functional rather than the conventional risk-neutral total
expected cost. Under some assumptions, we show that optimal, stationary,
Markovian policies exist and can be found via a special Bellman's equation. We
propose a computational technique based on difference convex programs (DCPs) to
find the associated value functions and therefore the risk-averse policies. A
rover navigation MDP is used to illustrate the proposed methodology with
conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent
risk measures.
