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Optimal portfolios with Haezendonck risk measures

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  • Bellini Fabio
  • Rosazza Gianin Emanuela

    (Universitá di Napoli, Dipartimento di Matematica e Statistica, Napoli, Italien)

Abstract

We deal with the problem of the practical use of Haezendonck risk measures (see Haezendonck and Goovaerts [8], Goovaerts et al. [7], Bellini and Rosazza Gianin [4]) in portfolio optimization. We first analyze the properties of the natural estimators of Haezendonck risk measures by means of numerical simulations and point out a connection with the theory of M-functionals (see Hampel [9], Huber [11], Serfling [19]) that enables us to derive analytic results on the asymptotic distribution of Orlicz premia. We then prove that as in the CVaR case (see Rockafellar and Uryasev [17,18], Bertsimas et al. [6]) the mean/Haezendonck optimal portfolios can be obtained through the solution of a single minimization, and that the resulting efficient frontiers are convex. We conclude with a real data example in which we compare optimal portfolios generated by a mean/Haezendonck criterion with mean/variance and mean/CVaR optimal portfolios.

Suggested Citation

  • Bellini Fabio & Rosazza Gianin Emanuela, 2008. "Optimal portfolios with Haezendonck risk measures," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 89-108, March.
    • Handle: RePEc:bpj:strimo:v:26:y:2008:i:2:p:89-108:n:3
    DOI: 10.1524/stnd.2008.0915
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    References listed on IDEAS

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    1. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
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    6. Bellini, Fabio & Rosazza Gianin, Emanuela, 2008. "On Haezendonck risk measures," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 986-994, June.
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    Cited by:

    1. Saul Jacka & Seb Armstrong & Abdelkarem Berkaoui, 2017. "On representing and hedging claims for coherent risk measures," Papers 1703.03638, arXiv.org, revised Feb 2018.
    2. Mao, Tiantian & Hu, Taizhong, 2012. "Second-order properties of the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 333-343.
    3. Zhiping Chen & Qianhui Hu & Ruiyue Lin, 2016. "Performance ratio-based coherent risk measure and its application," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 681-693, May.
    4. Ahn, Jae Youn & Shyamalkumar, Nariankadu D., 2014. "Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 78-90.
    5. Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
    6. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
    7. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.

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