We consider a classical risk process with arrival of claims following a stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article is to establish a diffusion approximation by verifying a functional central limit theorem and to compute the ruin probability in finite-time horizon . Numerical results will also be given.
R
stationary
non-stationary
R
this
the
D
of this model
R
both the
the ruin probability in
R
and infinite-time horizonruin probabilities
horizon