H. Zheng (UK)
heterogeneous portfolios, analytic approximation, risk measures.
In this paper we discuss the analytic approximation to the loss distribution of large conditionally independent hetero geneous portfolios. We first apply the Esseen's inequality to show that the overall loss distribution can be approxi mated accurately and computed efficiently by the integra tion of a normal distribution function. We then discuss the portfolio risk measures (VaR and CVaR) and show that they can be easily derived by solving a linear programming problem where VaR is the optimal solution and CVaR is the optimal value. Finally we illustrate with two examples that the analytic approximation is less suitable in studying the extreme value of tail distributions.
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