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The almost sure convergence rate of the estimator of optimized certainty equivalent risk measure under α-mixing sequences

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  • Zhongde Luo
  • Shide Ou

Abstract

Conditional value-at-risk (CVaR) model is a kind of financial risk measure that is extensively supported and accepted by international financial community. Its optimized form can be regarded as an optimized certainty equivalent (OCE) risk measurement. In this paper, we mainly discuss and analyze the strong laws of large numbers and the convergence rate of OCE's estimator under α-mixing sequences. The result shows that the almost sure convergence rate of CVaR estimator is given by the results of OCE estimator. Its convergence rate is inversely proportional to the square root of the sample size under certain conditions. Its effectiveness is verified by simulation experiments for two classical α-mixing sequences.

Suggested Citation

  • Zhongde Luo & Shide Ou, 2017. "The almost sure convergence rate of the estimator of optimized certainty equivalent risk measure under α-mixing sequences," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 8166-8177, August.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:16:p:8166-8177
    DOI: 10.1080/03610926.2016.1175630
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    Cited by:

    1. Zhongde Luo, 2020. "Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences," Statistical Papers, Springer, vol. 61(2), pages 615-643, April.

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