The Finite-Time Ruin Probability With Heavy-tailed And Date Simulation

Consider a discrete-time insurance risk model in which the insurer makes both risk-free and risky investments. Assume that the one-period insurance and financial risks form a se-quence of independent and identically distributed copies of a random pair (X, Y) with dependent components. When the product XY is heavy tailed, under a mild restriction on the dependence structure of (X, Y), we establish for the finite-time ruin probability an asymptotic formula, which coincides with the long-standing one in the literature. Various important special cases are pre-sented, showing that our work generalizes and unifies some of recent ones. The previous content described is one dimensional case, on the basis of which, we will extend the one-dimensional to the two-dimensional case, and some important conclusions are obtained. What's more, we do some date simulations for both one-dimensional case and two-dimensional case.