Abstract: We considered a class of stochastic premium risk model with investment income, and assumed that the interest rate process was a non-negative Lévy process. We obtained nonexponential upper bounds of the ruin probability by martingale and inductive approaches, respectively, and gave some numerical simulations to illustrate the advantage of the nonexponential upper bounds.

Key words: non-exponential upper bound, stochastic interest rate, stochastic premium, ruin probability