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In this paper, we investigate risk measures such as value at risk (VaR) andthe conditional tail expectation (CTE) of the extreme (maximum and minimum) andthe aggregate (total) of two dependent risks. In finance, insurance and theother fields, when people invest their money in two or more dependent orindependent markets, it is very important to know the extreme and total riskbefore the investment. To find these risk measures for dependent cases is quitechallenging, which has not been reported in the literature to the best of ourknowledge. We use the FGM copula for modelling the dependence as it isrelatively simple for computational purposes and has empirical successes. Themarginal of the risks are considered as exponential and pareto, separately, forthe case of extreme risk and as exponential for the case of the total risk. Theeffect of the degree of dependency on the VaR and CTE of the extreme and totalrisks is analyzed. We also make comparisons for the dependent and independentrisks. Moreover, we propose a new risk measure called median of tail (MoT) andinvestigate MoT for the extreme and aggregate dependent risks.

Estimating value at risk and conditional tail expectation for extreme and aggregate risks