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Optimal risk sharing with translation invariant recursive utility for jump-diffusions

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  • Aase, Knut K.

    (Dept. of Business and Management Science, Norwegian School of Economics)

Abstract

We consider optimal risk sharing where agents have preferences represented by translation invariant recursive utility. The dynamics in continuous time is driven by diffusion processes and a random jump measure. The model has some appealing features compared to the scale invariant version. Economic effects of sudden events, like catastrophes or pandemics, can be interpreted and separated from ordinary shocks to the economy. Unlike the scale invariant version, this model allows for a treatment of heterogeneous preferences, and consequently optimal risk sharing at a general and basic level. A new endogenous variable, a traded security, enters via the preference structure, affecting the key relations between agents. We also implement a stock market in this setting, and derive a consumption based capital asset model. A catastrophe-insurance forward contract is analyzed as an application of our general model, where the jump part is priced and plays the essential role.

Suggested Citation

  • Aase, Knut K., 2025. "Optimal risk sharing with translation invariant recursive utility for jump-diffusions," Discussion Papers 2025/5, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2025_005
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    References listed on IDEAS

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    1. Mark Schroder & Costis Skiadas, 2008. "Optimality And State Pricing In Constrained Financial Markets With Recursive Utility Under Continuous And Discontinuous Information," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 199-238, April.
    2. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    3. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
    4. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
    5. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    6. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    7. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    9. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    10. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
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    Keywords

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    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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