Ruin probabilities with compounding assets

We consider a classical surplus process modified by the action of a constant force of interest. We derive recursive algorithms for the calculation of the probability of ruin in finite time. We also discuss the numerical evaluation of the probability of ultimate ruin using methods proposed by De Vylder [De Vylder, F., 1996. Advanced Risk Theory. Editions de l’Université de Bruxelles.] and Sundt and Teugels [Sundt, B., Teugels, J.L., 1995. Insurance: Mathematics and Economics 16, 7–22]. Finally, we consider the problem of recovery from ruin.