Ruin and Dividend Measures in the Renewal Dual Risk Model

In this manuscript we consider the dual risk model with financial application, where random gains occur under a renewal process. We particularly work Erlang(n) case for common distribution of inter-arrival times, from there it is easy to understand that our method or procedures can be generalised other cases matrix-exponential family case. several and different problems involving future dividends ruin. also show results are valid even if usual income condition not satisfied. most known works model, main target study have been calculation expected discounted optimal strategies, dividend done on aggregate. find works, at first using classical compound Poisson then some examples Erlang models. Knowing ruin ultimately achieved, important should evaluated an individual basis, early contribution aggregate utmost importance. From calculations really see how much dividend. Afonso et al. (Insur Math Econ, 53(3), 906–918, 2013) had worked similar model. Besides explicit formulae both probability getting amount single still number reach given upper (like constant barrier) as well down complete working illustrative numerical final numbers study.