Upper Bound of Ruin Probability for an Insurance Discrete-Time Risk Model with Proportional Reinsurance and Investment

Two upper bounds for ruin probability under the discrete time risk model for insurance controlled by two factors: proportional reinsurance and surplus investment are presented. The latter is of interest because of the assumption that insurers invest some or their entire financial surplus on both the stock and bond markets, for which bond interest rates follow a time – homogeneous Markov chain. In addition, the control of reinsurance and stock investment in each time period are assumed to be constant values. The first upper bound for finite time ruin probability and ultimate ruin probability was derived under the condition that the Lundberg coefficient exists. The second upper bound is for finite time ruin probability and was developed from a new worse than used function. Numerical examples are used to illustrate these results, and the upper bound of ruin probability using real-life motor insurance claims data from a broker is also presented