A Numerical Comparison of the Insurer’s Ruin Probabilities under the Lundberg’s and Tijim’s Ruin Frameworks

Authors

  • G. M. Ogungbenle, S.K. Ogungbenle and A .T. Chakfa

Keywords:

Lundberg’s approximation, Tijim’s ruin, Gamma distribution, Initial capital, Survival probability, Safety loading

Abstract

Recently, the Nigerian insurance industry has experienced underwriting problems resulting from the insolvency of a few insurance firms. It becomes necessary to appraise the ruin probability of insurer’s portfolio of schemes so as to estimate the degree to which the insurer could survive. Classical models such as Lundberg’s inequality evolved to help obtain reasonable estimations of ruin. The classical model considers the effect of underwriting modifications such as loading factors to ensure that approximations in the model are worthwhile. When an insurance surplus falls below a prescribed benchmark, the insurer is technically ruined. This paper studies and compares ruin probabilities under Lundberg’s and Tijim’s models with gamma claims. The objectives of this study are: (i) to solve the adjustment co-efficient using the moment generating ‘’function,’’ (ii) to compute the Lundberg’s ‘’co-efficient,’’ (iii) to compute Tijim’s ruin approximation and then compare. Computational evidence from the results show that the Tijims approximation is lower and hence represents an improvement over Lundberg’s co-efficient. Furthermore, the results show that as the initial capital increases, the probability of ruin decreases under the two models. Further evidence also reveals that as the safety loading and the adjustment coefficient increase, the ruin probability decreases. From the foregoing, the results obtained could be employed to advise the insurance firms through the regulatory authorities to enshrine policy framework which can forestall pervasive consequences of ruin. Consequently, actuaries can use the results obtained to advise insurance operators on the minimum capital to avoid ruin conditions.

Author Biography

G. M. Ogungbenle, S.K. Ogungbenle and A .T. Chakfa

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Published

05/12/2024