risk estimation for the new heavy tail distribution using bayesian approach

This study addresses the evaluation of value-at-risk (var) using a bayesian approach, specifically employing the heavy-tailed weibull (htw) distribution. the var is a crucial financial metric for business and investment decision-making. while various methods exist for estimating var, this research focuses on statistical techniques utilizing heavy-tail distributions. the paper extends the heavy-tailed weibull model, which is particularly relevant for financial applications and provides reliable predictions for heavy-tailed data. the statistical properties of the htw distribution are developed and bayesian estimates under multiple symmetric and asymmetric loss functions are obtained. the bayes estimate is evaluated from the posterior distribution that minimizes the corresponding posterior risk. due to the complexity of the posterior distribution, the metropolis-hastings algorithm (mha) is implemented to draw posterior samples. the markov chain monte carlo sample convergence is evaluated through diagnostic plots. the insurance loss data is used to display the application of the presented methodology in a real-world situation. the outcomes showed that bayesian estimates can be used to evaluate the value-at-risk measure well. financial institutions and risk managers can consider implementing bayesian methods with heavy-tailed distributions, particularly the heavy-tailed weibull model, for more accurate var estimation. this approach is especially valuable for portfolios with extreme events or fat-tailed return distributions.