We present a unified approach to value at risk analysis under heavy-tailedness using new majorization theory for linear combinations of thick-tailed random variables that we develop. Among other results, we show that the stylized fact that portfolio diversification is always preferable is...

The present paper introduces new sign tests for testing for conditionally symmetric martingale-difference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that...