A Novel Insurance Claims (Revenues) Xgamma Extension: Distributional Risk Analysis Utilizing Left-Skewed Insurance Claims and Right-Skewed Reinsurance Revenues Data with Financial PORT-VaR Analysis

The continuous probability distributions can be successfully utilized to characterize and evaluate the risk exposure in applied actuarial analysis. Actuaries often prefer to convey the level of exposure to a certain hazard using merely a numerical value, or at the very least, a small number of numbers. In this paper, a new applied probability model was presented and used to model six different sets of data. About estimating the risks that insurance companies are exposed to and the revenues of the reinsurance process, we have analyzed and studied data on insurance claims and data on reinsurance revenues as an actuarial example. These actuarial risk exposure functions, sometimes referred to as main risk actuarial indicators, are unquestionably a result of a particular model that can be explained. Five crucial actuarial indicators are used in this study to identify the risk exposure in insurance claims and reinsurance revenues. The parameters are estimated using techniques like the maximum product spacing, maximum-likelihood, and least square estimation. Monte Carlo simulation research is conducted under a specific set of conditions and controls. Additionally, five actuarial risk indicators including the value-at-risk, tail-variance, tail value-at-risk, tail mean-variance, and mean of the excess loss function, were utilized to explain the risk exposure in the context of data on insurance claims and reinsurance revenue. The peak over a random threshold value-at-risk (PORT-VaR) approach and value-at-risk estimate are taken into account and contrasted for detecting the extreme financial insurance peaks.