Concentration inequality of sums of dependent subexponential random variables and application to bounds for value-at-risk

Concentration inequalities are widely used tools in many fields such as high-dimensional statistics, machine learning, optimization, signal processing, time series analysis, and finance. Therefore, various types of concentration inequalities have been derived so far. In this study, we derived new concentration inequalities for the sum of subexponential random variables. First one is the concentration inequalities for the sum of subexponential random variables with partial dependence structure. Second one is the concentration inequalities with Pearson's phi. By applying obtained concentration inequalities to the problem of portfolio risk management, we obtained upper bound for the value-at-risk of financial portfolio.