Random Premiums Risk Process with Dividends and Investment

We extend the discrete time risk model studied in [1] by introducing an investment component and show that the combined dividend-investment model provides higher expected returns for both the insurer and the shareholders. Furthermore, we show that given two strategies that have the same probability of ultimate ruin on the infinite time horizon, the strategy with larger initial capital and smaller loading factor is less risky than the strategy with smaller initial capital and larger loading factor in that it has a smaller lower bound for ruin probability on the finite time horizon.