On the Distribution of Discounted Collective Risk Model

We study the distribution of discounted collective risk model where the counting process is Poisson. For the model considered here, we obtain mean, variance and moment generating function (m.g.f) of the model. To do this, we use two approaches. In the first approach we use classical methods to obtain the mean and variance. In the second approach we introduce some proper martingale and then we obtain the m.g.f of total loss by features of martingales. Additionally, we use Fast Fourier Transform to numerically calculate the distribution of discounted collective risk model.