Description: Sometimes, rare things happen and the least expected occurs. Indeed, some events occur once or twice in a lifetime leaving little room to learn from experiences. In financial markets, extreme events, no matter how rare, could have a profound impact on a company or even the whole country. Insurers are also not free from the impact of catastrophic large-scale extreme events. As a result, with pervasive economic and financial revolutions sweeping our world and potential devastative catastrophes, the increasing interest in tail risk management is fuelled by practical issues, including investment downside risk and insurance catastrophe risk. Thus, developing statistical techniques to model extreme investment and insurance losses is certainly a major task for risk managers. the purpose of our paper is to apply moment methods to estimate the joint events such as concurrent extreme investment loss and insurance loss. A novel aspect of this article is that it takes into account the correlation between different assets and insurance lines of business.