Optimal Expected Utility Risk Measures

Geissel, Sebastian; Sass, Jörn; Seifried, Frank Thomas

doi:10.2139/ssrn.2651132

Cited by 3 publications

(4 citation statements)

References 31 publications

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“…Feasible and desirable extensions for future research are (i) to re-examine the rationality of our axioms considering other risk measures in rankdependent expected utility theory such as the optimal expected utility risk measures as in the study by Geissel, Sass, and Seifried (2018) and the extreme risk aggregation approach as in the study by Chen and Hu (2019);…”

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

Koumou

Dionne

2019

SSRN Journal

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We provide an axiomatic foundation for the measurement of correlation diversification measures in a one-period portfolio model. We propose a set of nine desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures which we distinguish from coherent risk measures. We provide the decision theoretic foundations of our axioms by studying their compatibility with investors' preference for diversification in rank-dependent expected utility theory. We examine some of the most frequently used methods for measuring correlation diversification in terms of our axioms. Lastly, we explore whether our axioms have a representation function.

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Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

Koumou

Dionne

2019

SSRN Journal

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“…The theoretical setup and notations are, with respect to risk measures, similar to (Geissel et al;. With the filtration (F) 0≤t≤T , T > 0 that is fixed on the probability space (Ω, F, P) in such a way that F 0 = {∅, Ω} and F T = F, we can specify a financial position X ∶ Ω → R as a random variable on the probability space (Ω, F, P).…”

Section: Setup and Notationsmentioning

confidence: 99%

“…Example 2. Given a utility function u, the optimal expected utility risk measure is introduced in Geissel et al (2017)…”

Section: Setup and Notationsmentioning

confidence: 99%

“…The supremum in (OEU) is attained uniquely at η * X ∈ [−X min ,∞). We refer to (Geissel et al; for proofs of the aforementioned properties and for a natural economic interpretation for (OEU) in terms of risk capital. OEU considers the entire information of return distributions, while downside risk measures such as V@R consider only parts of the distribution.…”

Section: Setup and Notationsmentioning

confidence: 99%

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Portfolio Optimization with Optimal Expected Utility Risk Measures

Fink

Geissel

Herbinger³

et al. 2019

SSRN Journal

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The purpose of this article is to evaluate optimal expected utility risk measures (OEU) in a riskconstrained portfolio optimization context where the expected portfolio return is maximized. We compare the portfolio optimization with OEU constraint to a portfolio selection model using value at risk as constraint. The former is a coherent risk measure for utility functions with constant relative risk aversion and allows individual specifications to the investor's risk attitude and time preference. In a case study with three indices we investigate how these theoretical differences influence the performance of the portfolio selection strategies. A copula approach with univariate ARMA-GARCH models is used in a rolling forecast to simulate monthly future returns and calculate the derived measures for the optimization. The results of this study illustrate that both optimization strategies perform considerably better than an equally weighted portfolio and a buy and hold portfolio. Moreover, our results illustrate that portfolio optimization with OEU constraint experiences individualized effects, e.g. less risk averse investors lose more portfolio value in the financial crises but outperform their more risk averse counterparts in bull markets.

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