IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2508.16600.html
   My bibliography  Save this paper

Higher moments under dependence uncertainty with applications in insurance

Author

Listed:
  • Carole Bernard
  • Jinghui Chen
  • Steven Vanduffel

Abstract

Recent studies have highlighted the significance of higher-order moments - such as coskewness - in portfolio optimization within the financial domain. This paper extends that focus to the field of actuarial science by examining the impact of these moments on key actuarial applications. In the first part, we derive analytical lower and upper bounds for mixed moments of the form $\mathbb{E}(X_1X_2^d)$, where $X_i \sim F_i$ for $i=1,2$, assuming known marginal distributions but unspecified dependence structure. The results are general and applicable to arbitrary marginals and positive integer orders $d$, and we also identify the dependence structures that attain these bounds. These findings are then applied to bound centered mixed moments and explore their mathematical properties. The second part of the paper investigates the influence of higher-order centered mixed moments on key actuarial quantities, including expected shortfall (ES), marginal expected shortfall (MES), and life annuity valuation. Under a copula-based mixture model, we show that coskewness and other odd-order mixed moments exhibit a monotonic relationship with both ES and annuity premiums. However, the effect on MES is more nuanced and may remain invariant depending on the underlying dependence structure.

Suggested Citation

  • Carole Bernard & Jinghui Chen & Steven Vanduffel, 2025. "Higher moments under dependence uncertainty with applications in insurance," Papers 2508.16600, arXiv.org.
    • Handle: RePEc:arx:papers:2508.16600
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2508.16600
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2508.16600. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.