Chini's equations in actuarial mathematics

Abstract. We deal with an equation mentioned by M. Chini in [3] and recalled by A. Guerraggio in [6]. This is a multiplicative form of the equation previously studied by T. Riedel, P. K. Sahoo and the second author (cf. [9]). We solve it completely in the case where sets of zeros of the unknown functions are nonempty, under very mild assumptions. In the remaining case, we reduce the problem to the one considered in [9].