Threshold Net Profit Condition in Predicting the Insurer’s Probability of Ruin

Abstract

Purpose: An insurer is technically ruined when its surplus falls below a specified level that is less than a defined benchmark. In ruin analysis, the classical Lundberg’s model describes the claim’s process of an insurer where the claim size and the inter-arrival times are independent of each other, but this may not be reasonable enough since it is complex to express the adjustment coefficient in terms of the distributions of claim sizes and inter-arrival times. It is, therefore, reasonable to compare the ruin probability of insurer’s portfolio under Tijim’s approximation in order to determine the level at which the insurer could survive. The objectives of this study are to estimate the adjustment coefficient using moment generating function, confirm when the net profit condition is violated and construct model for the exponential parameter of the Tijim’s model. Design/Methodology/Approach: We compare ruin probabilities Lundberg’s and Tijim’s frameworks under Gamma claims. Findings: Computational evidence from the results reveals that Tijim’s approximation is comparatively lower than Lundberg’s upper bound and, therefore, represents an improvement. The empirical analysis suggests that the insurer should avoid initial reserve below 1,800,000.00. From tables 2 and 3, at any level of the initial capital u both models seem not converging to zero very fast. Within the interval 1000000 ≤ u ≤ 1800000, the ruin probability is trivially confirming that the net profit condition E(X) − a < 0 is violated. Originality: This paper has improved the Tijim’s estimation analytically as demonstrated in our empirical analysis.