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 indepen-dent and identically distributed random pairs with common bivariate Farlie–Gumbel– Morgenstern (FGM) distribution. The parameter θ of the FGM distribution governs the strength of dependence, with a smaller value of θ corresponding to a less risky situation. For the subexponential case with −1 < θ ≤ 1, a general asymptotic for-mula 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 quan-titative understanding on how significantly the asymptotic ruin probability decreases when θ switches from its normal range to its negative extremum