Asymptotics for a discrete-time risk model with Gamma-like insurance risks

Consider a discrete-time insurance risk model with insurance and financial risks. Within period i$ i $, the net insurance loss is denoted by Xi$ X_i $ and the stochastic discount factor over the same time period is denoted by Yi$ Y_i $. Assume that {Xi,i≥1}$ \{X_i,\ i \ge 1\} $ form a sequence of independent and identically distributed real-valued random variables with common distribution F$ F $; {Yi,i≥1}$ \{Y_i,\ i \ge 1\} $ are another sequence of independent and identically distributed positive random variables with common distribution G$ G $; and the two sequences are mutually independent. Under the assumptions that F$ F $ is Gamma-like tailed and G$ G $ has a finite upper endpoint, we derive some precise formulas for the tail probability of the present value of aggregate net losses and the finite-time and infinite-time ruin probabilities. As an extension, a dependent risk model is considered, where each random pair of the net loss and the discount factor follows a bivariate Sarmanov distribution.