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Confidence band for expectation dependence with applications

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  • Guo, Xu
  • Li, Jingyuan

Abstract

Motivated by the applications of the concept of expectation dependence in economics and finance, we propose a method to construct uniform confidence band for expectation dependence. It is derived based on Hoeffding’s inequality. Our proposed confidence band can be explicitly expressed and thus it is very easy to implement. Our method has applications to demand for a risky asset and first-order risk aversion problems. Simulations suggest our proposed confidence interval can control the coverage probabilities very well, and the average lengths are very short. Two empirical applications are presented to illustrate the usefulness of the constructed confidence band of expectation dependence.

Suggested Citation

  • Guo, Xu & Li, Jingyuan, 2016. "Confidence band for expectation dependence with applications," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 141-149.
    • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:141-149
    DOI: 10.1016/j.insmatheco.2015.09.012
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    References listed on IDEAS

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    1. Kit Pong Wong, 2012. "Production and hedging under state‐dependent preferences," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(10), pages 945-963, October.
    2. Kit Wong, 2014. "Production and hedging in futures markets with multiple delivery specifications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 413-421, October.
    3. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.
    4. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.
    5. Michel Denuit & Rachel Huang & Larry Tzeng, 2015. "Almost expectation and excess dependence notions," Theory and Decision, Springer, vol. 79(3), pages 375-401, November.
    6. Wong, Kit Pong, 2012. "Production and futures hedging with state-dependent background risk," International Review of Economics & Finance, Elsevier, vol. 24(C), pages 177-184.
    7. Wong, Kit Pong, 2013. "Fixed versus variable rate loans under state-dependent preferences," Economic Modelling, Elsevier, vol. 31(C), pages 659-663.
    8. Dhaene, Jan & Denuit, Michel & Vanduffel, Steven, 2009. "Correlation order, merging and diversification," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 325-332, December.
    9. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    10. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    11. Kit Wong, 2014. "Hedging and the competitive firm under correlated price and background risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 329-340, October.
    12. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    13. Soon Koo Hong & Keun Ock Lew & Richard MacMinn & Patrick Brockett, 2011. "Mossin's Theorem Given Random Initial Wealth," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 309-324, June.
    14. Loomes, Graham & Segal, Uzi, 1994. "Observing Different Orders of Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 239-256, December.
    15. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.
    16. Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 422-450.
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    Cited by:

    1. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 163-172.
    2. Zaunbrecher, Barbara S. & Linzenich, Anika & Ziefle, Martina, 2017. "A mast is a mast is a mast…? Comparison of preferences for location-scenarios of electricity pylons and wind power plants using conjoint analysis," Energy Policy, Elsevier, vol. 105(C), pages 429-439.
    3. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Discussion Papers ISBA 2021021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    Keywords

    Confidence band estimation; Demand for a risky asset; Expectation dependence; First-order risk aversion; Hoeffding’s inequality;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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