Lower and Upper Bounds of the Ultimate Ruin Probability in a Discrete Time Risk Model with Proportional Reinsurance and Investment

  • Apichart Luesamai Phranakhon Rajabhat University, Thailand
Keywords: Bound of Ruin Probability, Discrete Time Risk Model, Reinsurance and Investment


The lower and upper bounds of the ultimate ruin probability in a discrete time risk model with proportional reinsurance and investment are determined under the assumption that the reinsurance retention level and the amount of investment in a particular stock during each time period can remain constant by employing integral operator L. The lower bound is obtained from the finite time ruin probability that converges to the ultimate ruin probability with increasing time while the upper bound is iteratively determined by using Luesamai and Chongcharoen’s upper bound as the starting point. Besides, the ultimate ruin probability as a fixed point of L is illustrated.