In this study, the two upper bounds of the ruin probability for discrete time risk model derived by adding two controlled factors to the classical discrete time risk model: proportional reinsurance and investment are proposed. These upper bounds are derived using an inductive method and rely on a recursive form of the finite time and/or an integral equation of ultimate (infinite time) of ruin probability which is also derived in this study. Both of the upper bounds are formulated by the assumption that the retention level of reinsurance and ...