Abstract.
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 L1.
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.
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Mathematics Subject Classification:
91B16, 91B28
JEL Classification:
C60, G13
The first author thanks Walter Schachermayer for an invitation to the TU Vienna and financial support.
The second author thanks Peter Grandits for fruitful discussions and encouragement. Financial Support by the Austrian National Bank, Jubiläumsfond 8699, and by the FWF, SFB 010 is gratefully acknowledged.
Both authors are thankful for valuable comments by an anonymous referee.
Manuscript received: June 2003; final version received: May 2005
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Cheridito, P., Summer, C. Utility maximization under increasing risk aversion in one-period models. Finance Stochast. 10, 147–158 (2006). https://doi.org/10.1007/s00780-005-0164-9
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DOI: https://doi.org/10.1007/s00780-005-0164-9