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Media type:
E-Article
Title:
Optimal Strategies and Utility-Based Prices Converge When Agents' Preferences Do
Contributor:
Carassus, Laurence;
Rásonyi, Miklós
imprint:
Institute for Operations Research and the Management Sciences, 2007
Published in:Mathematics of Operations Research
Language:
English
ISSN:
0364-765X;
1526-5471
Origination:
Footnote:
Description:
<p>A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions<tex-math>$U_{n}$</tex-math>, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever<tex-math>$U_{n}$</tex-math>tends to another utility function<tex-math>$U_{\infty}$</tex-math>, the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price of Davis [Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derative Securities. Cambridge University Press, pp. 216-226] and the utility indifference price of Hodges and Neuberger [Hodges, R., K. Neuberger. 1989. Optimal replication of contingent claims under transaction costs. Rev. Futures Markets 8 222-239] with respect to changes in agents' preferences.</p>