Minimizing risk models in stochastic shortest path problems

We consider a minimizing risk model in a stochastic shortest path problem in which for each node of a graph we select a probability distribution over the set of successor nodes so as to reach a given target node with minimum threshold probability. We formulate such a problem as undiscounted finite Markov decision processes. We show that an optimal value function is a unique solution to an optimality equation and find an optimal stationary policy. A value iteration method is also given.