Ruin with insurance and financial risks following the least risky FGM dependence structure

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 θ of the FGMdistribution governs the strength of dependence, with a smaller value of θ corresponding to a less risky situation. For the subexponential casewith−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 = −1. In this paper, we complete the study by extending it to θ = −1. The new formulas for θ = −1 look very different from, but are intrinsically consistent with, the existing one for −1 < θ ≤ 1, and they offer a quantitative understanding on how significantly the asymptotic ruin probability decreases when θ switches from its normal range to its negative extremum. © 2015 Elsevier B.V. All rights reserved.