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Utility-based acceptability indices

Author

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  • Marcin Pitera
  • Mikl'os R'asonyi

Abstract

In this short paper we introduce a new class of performance measures based on certainty equivalents defined via scaled utility functions. We analyse their properties, show that the corresponding portfolio optimization problem is well-posed under generic conditions, and analyse the link between portfolio dynamics, benchmark process, and utility function choice in the long-run setting.

Suggested Citation

  • Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    • Handle: RePEc:arx:papers:2310.02014
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    File URL: http://arxiv.org/pdf/2310.02014
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    References listed on IDEAS

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    1. Rolando Cavazos-Cadena, 2010. "Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 47-84, February.
    2. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2013. "Dynamic Conic Finance: Pricing And Hedging In Market Models With Transaction Costs Via Dynamic Coherent Acceptability Indices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-36.
    3. Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    4. Tomasz R. Bielecki & Stanley R. Pliska, 2003. "Economic Properties of the Risk Sensitive Criterion for Portfolio Management," Review of Accounting and Finance, Emerald Group Publishing Limited, vol. 2(2), pages 3-17, February.
    5. Marcin Pitera & Thorsten Schmidt, 2020. "Estimating and backtesting risk under heavy tails," Papers 2010.09937, arXiv.org, revised Jan 2022.
    6. Pitera, Marcin & Schmidt, Thorsten, 2022. "Estimating and backtesting risk under heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 1-14.
    7. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    8. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
    9. Rolando Cavazos-Cadena & Daniel Hernández-Hernández, 2016. "A Characterization of the Optimal Certainty Equivalent of the Average Cost via the Arrow-Pratt Sensitivity Function," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 224-235, February.
    10. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    11. Marcin Pitera & Łukasz Stettner, 2016. "Long run risk sensitive portfolio with general factors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 265-293, April.
    12. Marcin Pitera & Thorsten Schmidt, 2022. "Estimating and backtesting risk under heavy tails," Papers 2201.10454, arXiv.org, revised Jan 2022.
    13. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    14. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    15. Aharon Ben-Tal & Marc Teboulle, 1986. "Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming," Management Science, INFORMS, vol. 32(11), pages 1445-1466, November.
    16. Paolo Guasoni & Lóránt Nagy & Miklós Rásonyi, 2021. "Young, timid, and risk takers," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1332-1356, October.
    17. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
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    Cited by:

    1. Salvucci, Vincenzo & Tarp, Finn, 2024. "Crises, prices, and poverty – An analysis based on the Mozambican household budget surveys 1996/97–2019/20," Food Policy, Elsevier, vol. 125(C).

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