Large deviations for affine diffusion processes on R+m×Rn

This paper proves the large deviation principle for affine diffusion processes with initial values in the interior of the state space R+m×Rn. We approach this problem in two different ways. In the first approach, we first prove the large deviation principle for finite dimensional distributions, and then use it to establish the sample path large deviation principle. For this approach, a more careful examination of the affine transform formula is required. The second approach exploits the exponential martingale method of Donati-Martin et al. for the squares of Ornstein–Uhlenbeck processes. We provide an application to importance sampling of affine diffusion models.