  Affine point processes are a class of simple point processes with self- and
mutually-exciting properties, and they have found useful applications in
several areas. In this paper, we obtain large-time asymptotic expansions in
large deviations and refined central limit theorem for affine point processes,
using the framework of mod-phi convergence. Our results extend the large-time
limit theorems in [Zhang et al. 2015. Math. Oper. Res. 40(4), 797-819]. The
resulting explicit approximations for large deviation probabilities and tail
expectations can be used as an alternative to importance sampling Monte Carlo
simulations. Numerical experiments illustrate our results.
