Uniform asymptotics of the finite-time ruin probability for all times

In this paper, we study the asymptotics of the finite-time ruin probability for a generalized renewal risk model with independent strong subexponential claim sizes and widely lower orthant dependent inter-occurrence times. This widely lower orthant dependence structure can include some common negative dependent random variables (r.v.s) such as negatively lower orthant dependent r.v.s, some positive dependent r.v.s and some other dependent r.v.s. For this generalized renewal risk model, we show that the asymptotics of the finite-time ruin probability hold uniformly for all times in the sense that the magnitude of the initial reserve of some insurance portfolio does not influence the length of the operating time. Further, the uniform asymptotics of the random-time ruin probability in the above model have been obtained.