Two examples of non strictly convex large deviations

TL;DR

This paper provides two examples of large deviations principles with non-strictly convex rate functions, including a financial model, and compares their rate functions under different contraction principles.

Contribution

It introduces new instances of non-strictly convex large deviations and analyzes their rate functions in the context of the Heston model.

Findings

Rate functions are not strictly convex in the presented examples.

The rate function for the Heston model matches the Freidlin-Wentzell rate function under contraction.

Adds to the understanding of large deviations in financial models.

Abstract

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.