Duality theory for concavification of utility functions in incomplete market model

Authors

DOI:

https://doi.org/10.17721/1812-5409.2021/2.2

Keywords:

standard utility maximization, robust utility maximization, optimal investments, non-concave utility, concavification

Abstract

The main goal for this paper is to prove the existence of the optimal investment strategies for the standard and robust problems of maximization for the concavified utility function in an incomplete market model. We extend the existing results for strictly concave utility functions to concavification of non-concave utility functions. Moreover, we present an assumption under which the optimal strategies for concavified problems are also optimal strategies for non-concave problems.

Pages of the article in the issue: 10 - 17

Language of the article: English

References

Reichlin, Christian Rochus August: "Utility Maximization with a Given Pricing Measure When the Utility Is Not Necessarily Concave"; Mathematics and Financial Economics, Volume 7, Issue 4, pp 531-556, 2013.

Delbaen, F., Schachermayer, W. A general version of the fundamental theorem of asset pricing. Math. Ann. 300 (1994), no. 3, 463-520.

Schied, Alexander; Wu, Ching-Tang. Duality theory for optimal investments under model uncertainty.

Kramkov, D., Schachermayer, W. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9, no. 3, 904-950 (1999).

Kramkov, D., Schachermayer, W. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab., Vol. 13, no. 4 (2003).

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Published

2021-11-04

Issue

Section

Algebra, Geometry and Probability Theory

How to Cite

Bahchedjioglou, O. O. (2021). Duality theory for concavification of utility functions in incomplete market model. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, 2, 10-17. https://doi.org/10.17721/1812-5409.2021/2.2