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Affine long term yield curves: An application of the Ramsey rule with progressive utility

Author

Listed:
  • Nicole El Karoui

    (LPMA, UMR CNRS 6632, Université Pierre et Marie Curie, France;
    CMAP, UMR CNRS 7641, école Polytechnique, France)

  • Caroline Hillairet

    (CMAP, UMR CNRS 7641, école Polytechnique, France)

  • Mohamed Mrad

    (LAGA, UMR CNRS 7539, Université Paris 13, France)

Abstract

The purpose of this paper relies on the study of long-term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.

Suggested Citation

  • Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Affine long term yield curves: An application of the Ramsey rule with progressive utility," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-24.
  • Handle: RePEc:wsi:jfexxx:v:01:y:2014:i:01:n:s2345768614500032
    DOI: 10.1142/S2345768614500032
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    References listed on IDEAS

    as
    1. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    2. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    3. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    4. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
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    Citations

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    Cited by:

    1. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2022. "Ramsey rule with forward/backward utility for long-term yield curves modeling," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 375-414, June.
    2. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2020. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Post-Print hal-00974815, HAL.
    3. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    4. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    5. Edouard Debonneuil & Anne Eyraud-Loisel & Frédéric Planchet, 2018. "Can Pension Funds Partially Manage Longevity Risk by Investing in a Longevity Megafund?," Risks, MDPI, vol. 6(3), pages 1-27, July.
    6. Bensusan, Harry & El Karoui, Nicole & Loisel, Stéphane & Salhi, Yahia, 2016. "Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 61-72.
    7. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    8. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Post-Print hal-01728554, HAL.
    9. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2019. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Post-Print hal-01721441, HAL.
    10. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Working Papers hal-01728554, HAL.
    11. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Working Papers hal-01721441, HAL.

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    1. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Post-Print hal-00974831, HAL.
    2. Edouard Debonneuil & Anne Eyraud-Loisel & Frédéric Planchet, 2018. "Can Pension Funds Partially Manage Longevity Risk by Investing in a Longevity Megafund?," Risks, MDPI, vol. 6(3), pages 1-27, July.
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    4. Bensusan, Harry & El Karoui, Nicole & Loisel, Stéphane & Salhi, Yahia, 2016. "Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 61-72.
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    6. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    7. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
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    12. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Post-Print hal-01728554, HAL.

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