  We present two examples of a large deviations principle where the rate
function is not strictly convex. This is motivated by a model used in
mathematical finance (the Heston model), and adds a new item to the zoology of
non strictly convex large deviations. For one of these examples, we show that
the rate function of the Cramer-type of large deviations coincides with that of
the Freidlin-Wentzell when contraction principles are applied.
