Asymptotics for random-time ruin probability of a risk model with diffusion, constant interest force and non-stationary arrivals

Consider an insurance risk model with diffusion, constant interest force and non -stationary arrivals, where the claims arrive according to a non-stationary process satisfying a large deviation principle. The asymptotic formula for the random-time ruin probability is ob-tained if the claim-size distribution is subexponential. Furthermore, with a certain dependence structure among claim sizes, the formula still holds if the claim-size distribution belongs to the class with long tails and dominatedly varying tails.