The Mean Time for a Net Profit and the Probability of Ruin Prior to that Profit in the Classical Risk Model

For the classical risk model, we consider the expected amount of time until the insurer makes a net profit exceeding a prescribed amount a. Since ruin may occur prior to that event, we also discuss the probability of net profit for the insurer of at least a before ruin occurs. Finally, we derive an expression for the conditional expectation of the time to reach a certain profit given that this happens prior to ruin.

KEYWORDS: Stopping time, independent stationary increments, random walk, ruin probability.