General Freidlin–Wentzell Large Deviations and positive diffusions

Abstract

We prove Freidlin–Wentzell Large Deviation estimates under rather minimal assumptions. This allows one to derive Wentzell–Freidlin Large Deviation estimates for diffusions on the positive half line with coefficients that are neither bounded nor Lipschitz continuous. This applies to models of interest in Finance, i.e. the CIR and the CEV models, which are positive diffusion processes whose diffusion coefficient is only Hölder continuous.