Necessary and sufficient conditions in the problem of optimal investment in incomplete markets

Kramkov, D.; Schachermayer, W.

Ann. Appl. Probab., Tome 13 (2003) no. 1, p. 1504-1516 / Harvested from Project Euclid

Résumé

Following Ann. Appl. Probab. 9 (1999) 904--950 we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In the previous paper we proved that a minimal condition on the utility function alone, that is, a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite.

Publié le : 2003-11-14
Classification: Utility maximization, incomplete markets, Legendre transformation, duality theory, 90A09, 90A10, 90C26

@article{1069786508,
     author = {Kramkov, D. and Schachermayer, W.},
     title = {Necessary and sufficient conditions in the problem of optimal investment in incomplete markets},
     journal = {Ann. Appl. Probab.},
     volume = {13},
     number = {1},
     year = {2003},
     pages = { 1504-1516},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069786508}
}

Kramkov, D.; Schachermayer, W. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp.  1504-1516. http://gdmltest.u-ga.fr/item/1069786508/