Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks

This paper investigates the probability of ruin within finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset. Under assumption that the risks are heavy tailed, some precise estimates for the finite time ruin probability are derived, which confirm a folklore that the ruin probability is mainly determined by whichever of insurance risk and financial risk is heavier than the other. In addition, some discussions on the heavy tails of the sum and product of independent random variables are involved, most of which have their own merits.