2021/01/28 by Suman Thapa, Thapa, Suman, Yiqiang Q. Zhao +1
Decision Sciences · Economics, Econometrics and Finance · #62P05 #FOS: Economics and business #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2101.12402
openalex publication_date 2021/01/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we investigate risk measures such as value at risk (VaR) and\nthe conditional tail expectation (CTE) of the extreme (maximum and minimum) and\nthe aggregate (total) of two dependent risks. In finance, insurance and the\nother fields, when people invest their money in two or more dependent or\nindependent markets, it is very important to know the extreme and total risk\nbefore the investment. To find these risk measures for dependent cases is quite\nchallenging, which has not been reported in the literature to the best of our\nknowledge. We use the FGM copula for modelling the dependence as it is\nrelatively simple for computational purposes and has empirical successes. The\nmarginal of the risks are considered as exponential and pareto, separately, for\nthe case of extreme risk and as exponential for the case of the total risk. The\neffect of the degree of dependency on the VaR and CTE of the extreme and total\nrisks is analyzed. We also make comparisons for the dependent and independent\nrisks. Moreover, we propose a new risk measure called median of tail (MoT) and\ninvestigate MoT for the extreme and aggregate dependent risks.\n