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Utility indifference pricing and the Aumann–Serrano performance index

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  • Hodoshima, Jiro
  • Miyahara, Yoshio

Abstract

A performance index based on the economic index of riskiness by Aumann and Serrano (2008) can be derived from an index based on the utility indifference price with the exponential utility function. The exponential utility function is a special utility function and relevant when the associated investor is risk averse as well as risk loving. The index based on the utility indifference price with the exponential utility function becomes an index for the random variable g of gambles with the property E[g]>0 and P(g<0)>0 when the investor is risk averse and an index for the random variable g of gambles with the property E[g]<0 and P(g>0)>0 when the investor is risk loving. We provide sufficient conditions for the existence and uniqueness of the index when the investor is risk averse and risk loving.

Suggested Citation

  • Hodoshima, Jiro & Miyahara, Yoshio, 2020. "Utility indifference pricing and the Aumann–Serrano performance index," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 83-89.
    • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:83-89
    DOI: 10.1016/j.jmateco.2019.12.002
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    References listed on IDEAS

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    1. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    2. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    3. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    4. Jiro Hodoshima, 2019. "Stock performance by utility indifference pricing and the Sharpe ratio," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 327-338, February.
    5. Kadan, Ohad & Liu, Fang, 2014. "Performance evaluation with high moments and disaster risk," Journal of Financial Economics, Elsevier, vol. 113(1), pages 131-155.
    6. Schulze, Klaas, 2014. "Existence and computation of the Aumann–Serrano index of riskiness and its extension," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 219-224.
    7. Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
    8. Homm, Ulrich & Pigorsch, Christian, 2012. "An operational interpretation and existence of the Aumann–Serrano index of riskiness," Economics Letters, Elsevier, vol. 114(3), pages 265-267.
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    1. Hodoshima, Jiro, 2021. "The computational property of the Aumann–Serrano performance index under risk-averse and risk-loving preference," Finance Research Letters, Elsevier, vol. 39(C).
    2. Lu, Richard & Horng, Tzyy-Leng & Horng, Min-Sun & Wang, Amy Z.-H., 2023. "A performance evaluation of portfolio insurance under the Black and Scholes framework: An application of the economic index of riskiness," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 269-276.
    3. Hodoshima, Jiro & Yamawake, Toshiyuki, 2022. "Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes," International Review of Financial Analysis, Elsevier, vol. 83(C).
    4. Yoshio Miyahara, 2022. "Both Sensitive Value Measure and its Applications," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 357-379, June.
    5. Jiro Hodoshima & Toshiyuki Yamawake, 2022. "Comparing Dynamic and Static Performance Indexes in the Stock Market: Evidence From Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 171-193, June.

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