  We consider the problem of finding an optimal history-dependent routing
strategy on a directed graph weighted by stochastic arc costs when the
objective is to minimize the risk of spending more than a prescribed budget. To
help mitigate the impact of the lack of information on the arc cost probability
distributions, we introduce a robust counterpart where the distributions are
only known through confidence intervals on some statistics such as the mean,
the mean absolute deviation, and any quantile. Leveraging recent results in
distributionally robust optimization, we develop a general-purpose algorithm to
compute an approximate optimal strategy. To illustrate the benefits of the
robust approach, we run numerical experiments with field data from the
Singapore road network.
