In this paper, we investigate the optimal portfolio construction aiming at extracting the most diversification benefit. We employ the diversification ratio based on the Value-at-Risk as the measure of the diversification benefit. With modeling the dependence of risk factors by the multivariate regularly variation model, the most diversified portfolio is obtained by optimizing the asymptotic diversification ratio. Theoretically, we show that the asymptotic solution is a good approximation to the finite-level solution. Our theoretical results are supported by extensive numerical examples. By applying our portfolio optimization strategy to real market data, we show that our strategy provides a fast algorithm for handling a large portfolio, while outperforming other peer strategies in out-of-sample risk analyses.
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We are grateful to the Editor and two anonymous reviewers for their helpful comments and suggestions that have greatly improved the presentation of the paper. Hengxin Cui thanks the support from the Hickman Scholar Program of the Society of Actuaries . Ken Seng Tan acknowledges the research funding from the Society of Actuaries CAE's grant and the the Nanyang Technological University President's Chair in Actuarial Risk Management Grant (Grant Number: 021095-00001 ). Fan Yang acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (Grant Number: 04242 ).
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