ویرانی با بیمه و ریسک های مالی بدنبال حداقل ساختار وابستگی FGM مخاطره آمیز

Recently, Chen (2011) studied the finite-time ruin probability in a discrete-time risk model in which the insurance and financial risks form a sequence of independent and identically distributed random pairs with common bivariate Farlie–Gumbel–Morgenstern (FGM) distribution. The parameter θθ of the FGM distribution governs the strength of dependence, with a smaller value of θθ corresponding to a less risky situation. For the subexponential case with −1<θ≤1−1<θ≤1, a general asymptotic formula for the finite-time ruin probability was derived. However, the derivation there is not valid for the least risky case θ=−1θ=−1. In this paper, we complete the study by extending it to θ=−1θ=−1. The new formulas for θ=−1θ=−1 look very different from, but are intrinsically consistent with, the existing one for −1<θ≤1−1<θ≤1, and they offer a quantitative understanding on how significantly the asymptotic ruin probability decreases when θθ switches from its normal range to its negative extremum.