Tail behavior of discounted portfolio loss under upper tail comonotonicity

Consider an investment portfolio that is is crucially important for economic security and hence requires a prudent examination of discounted portfolio losses. Due to domino effects during financial crises or pandemics, individual losses may highly interplay and exhibit a strong coherence in the extremal dependence structure. Under the framework of upper tail comonotonicity, we carry out some asymptotic studies of aggregate discounted losses of a portfolio when individual losses are in the maximum domain of attractions of three extreme value distributions, respectively. Our main finding is, both analytically and numerically, that the tail dependence among individual losses has a significant impact on discounted portfolio loss, if ignored, may cause serious consequences to the portfolio risk management.