Duality theory for concavification of utility functions in incomplete market model
DOI:
https://doi.org/10.17721/1812-5409.2021/2.2Keywords:
standard utility maximization, robust utility maximization, optimal investments, non-concave utility, concavificationAbstract
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.
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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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