Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult … by a heavy-tailed background risk. A particular attention is given to the distortion and weighted risk measures and … allocations, as well as their special cases such as the conditional layer expectation, tail value at risk, and the truncated tail …

This paper investigates whether multivariate crash risk (MCRASH), defined as exposure to extreme realizations of … returns than stocks with low MCRASH. The premium is not explained by linear factor exposures, alternative downside risk … measures or stock characteristics. Extending market-based definitions of crash risk to other well-established factors helps to …