Ruin Probability Analysis in Automobile Insurance Using Gamma-Cubic Transmuted Exponential Distribution for Claim Severity

Insurance companies must confront and manage financial risks to ensure their survival. This article analyzes and manages risks by estimating ruin probability using the newly developed Gamma-Cubic Transmuted Exponential (GCTE) claim severity distribution. The GCTE distribution is obtained by mixing distribution and Cubic Rank Transmuted map techniques. Its parameters are estimated using the maximum likelihood estimation (MLE) method. The performance of GCTE distribution is compared with well-known loss distributions such as Gamma, Weibull, Lognormal, Inverse Gaussian, mixture Lognormal, and the Cubic Transmuted Exponential (CTE) distribution to identify the best-fitting distribution for claim severity data. To estimate ruin probability, a sample data simulation technique known as acceptance-rejection is employed in the surplus process. Additionally, the exponential function is used to predict the minimum capital reserve necessary to safeguard the company under acceptable risk levels. These methodologies aid decision-making and promote financial stability within non-life insurance companies.