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Utility maximization under increasing risk aversion in one-period models


  • Patrick Cheridito


  • Christopher Summer



It has been shown at different levels of generality that under increasing risk aversion utility indifference sell prices of a contingent claim converge to the super-replication price and the shortfalls of utility maximizing hedging portfolios starting from the super-replication price tend to zero in L 1 . In this paper we give an example of a one-period financial model with bounded prices where utility optimal strategies and terminal wealths stay bounded but do not converge when the risk aversion is going to infinity. Then we give general results on the behavior of utility maximizing strategies and terminal wealths under increasing risk aversion in one-period models. The concept of a balanced strategy turns out to play a crucial role. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Patrick Cheridito & Christopher Summer, 2006. "Utility maximization under increasing risk aversion in one-period models," Finance and Stochastics, Springer, vol. 10(1), pages 147-158, January.
  • Handle: RePEc:spr:finsto:v:10:y:2006:i:1:p:147-158
    DOI: 10.1007/s00780-005-0164-9

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    References listed on IDEAS

    1. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
    2. Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June.
    3. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
    4. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Paolo Guasoni & Constantinos Kardaras & Scott Robertson & Hao Xing, 2014. "Abstract, classic, and explicit turnpikes," Finance and Stochastics, Springer, vol. 18(1), pages 75-114, January.


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