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On Consistency of the Omega Ratio with Stochastic Dominance Rules

In: Innovations in Insurance, Risk- and Asset Management

Author

Listed:
  • Bernhard Klar
  • Alfred Müller

Abstract

Omega ratios have been introduced in [1] as a performance measure to compare the performance of different investment opportunities. It does not have some of the drawbacks of the famous Sharpe ratio. In particular, it is consistent with first order stochastic dominance. Omega ratios also have an interesting relation to expectiles, which found increasing interest recently as risk measures. There is some confusion in the literature about consistency with respect to second order stochastic dominance. In this paper, we clarify this and extend it to a consistency result with respect to stochastic dominance of order 1 + γ recently introduced in [2] and generalizing the classical concepts of stochastic dominance of first and second order. Several examples illustrate the usefulness of this result. Finally, some consistency results for even more general stochastic dominance rules are shown, including the concept of ϵ-almost stochastic dominance introduced in [3].

Suggested Citation

  • Bernhard Klar & Alfred Müller, 2018. "On Consistency of the Omega Ratio with Stochastic Dominance Rules," World Scientific Book Chapters, in: Kathrin Glau & Daniël Linders & Aleksey Min & Matthias Scherer & Lorenz Schneider & Rudi Zagst (ed.), Innovations in Insurance, Risk- and Asset Management, chapter 14, pages 367-380, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813272569_0014
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    Cited by:

    1. Balter, Anne G. & Chau, Ki Wai & Schweizer, Nikolaus, 2024. "Comparative risk aversion vs. threshold choice in the Omega ratio," Omega, Elsevier, vol. 123(C).

    More about this item

    Keywords

    Insurance; Actuarial Science; Risk Measure; Reinsurance; Copula; Replicating Portfolio; Bayesian Finance; Risk Classification; Stochastic Dominance; Dynamic Hedging; Autoregressive Hidden Markov Models; Exchange-Traded Funds; Uncertainty Quantification; Fixed Income; Stochastic Processes for Finance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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