  In this manuscript we consider the dual risk model with financial
application, where the random gains occur under a renewal process. We
particularly work the Erlang(n) case for common distribution of the
inter-arrival times, from there it is easy to understand that our method or
procedures can be generalised to other cases under the matrix-exponential
family case. We work several and different problems involving future dividends
and ruin. We also show that our results are valid even if the usual income
condition is not satisfied. In most known works under the dual model, the main
target under study have been the calculation of expected discounted future
dividends and optimal strategies, where the dividend calculation have been done
on aggregate. We can find works, at first using the classical compound Poisson
model, then some examples of other renewal Erlang models. Knowing that ruin is
ultimately achieved, we find important that dividends should be evaluated on an
individual basis, where the early dividend contribution for the aggregate are
of utmost importance. From our calculations we can really see how much
important is the contribution of the first dividend. Afonso et al. (2013) had
worked similar problems for the classical compound Poisson dual model. Besides
that we find explicit formulae for both the probability of getting a dividend
and the distribution of the amount of a single dividend. We still work the
probability distribution of the number of gains to reach a given upper target
(like a constant dividend barrier) as well as for the number of gains down to
ruin. We complete the study working some illustrative numerical examples that
show final numbers for the several problems under study.
