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May 2003 A complete explicit solution to the log-optimal portfolio problem
Thomas Goll, Jan Kallsen
Ann. Appl. Probab. 13(2): 774-799 (May 2003). DOI: 10.1214/aoap/1050689603


D. Kramkov and W. Schachermayer [Ann. Appl. Probab. 9 (1999) 904-950] proved the existence of log-optimal portfolios under weak assumptions in a very general setting. For many--but not all--cases, T. Goll and J. Kallsen [Stochastic Process. Appl. 89 (2000) 31-48] obtained the optimal solution explicitly in terms of the semimartingale characteristics of the price process. By extending this result, this paper provides a complete explicit characterization of log-optimal portfolios without constraints.

Moreover, the results of Goll and Kallsen are generalized here in two further respects: First, we allow for random convex trading constraints. Second, the remaining consumption time--or more generally the consumption clock--may be random, which corresponds to a life-insurance problem.

Finally, we consider neutral derivative pricing in incomplete markets.


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Thomas Goll. Jan Kallsen. "A complete explicit solution to the log-optimal portfolio problem." Ann. Appl. Probab. 13 (2) 774 - 799, May 2003.


Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1034.60047
MathSciNet: MR1970286
Digital Object Identifier: 10.1214/aoap/1050689603

Primary: 91B28
Secondary: 60G48 , 91B16

Keywords: life insurance , logarithmic utility , neutral derivative pricing , Portfolio optimization , semimartingale characteristics

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 2 • May 2003
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