Numerical calculation of finite-time ruin probabilities in the dual risk model

In the dual risk model, while the ultimate ruin probability has an exact and straightforward formula, the mathematics becomes significantly more complex when considering a finite time horizon, and the literature on this topic is scarce. As a result, there is a need for numerical approximations. To address this, we develop two numerical algorithms that can accommodate a wide range of distributions for the amount of individual earnings with minimal adjustments. These algorithms are grounded in the methodologies proposed by Cardoso and Egídio dos Reis (2002) and De Vylder and Goovaerts (1988), which involve approximating the continuous risk process with a discrete-time Markov chain framework. We work out some examples, providing approximate values for the density of the time to ruin, and we compare, in the long run, our approximations with the exact values for the ultimate ruin probability to evaluate their accuracy. We also benchmark our results against the few existing figures available in the literature. Our findings suggest that the proposed approaches offer an efficient and flexible methodology for computing finite-time ruin probabilities in the dual risk model.