Abstract
he 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.
Highlights
The optimal investment problem is one of the most actual problem nowadays
There is a lot of aspects that can be considered in this problem such as the concavity of utility function, market model, the assumptions on the value process, the set of probability measures and the possibility of constructing the optimal investment strategies etc
We consider the discounted price process with d assets which modeled by a stochastic process S = (St)0 t T
Summary
The optimal investment problem is one of the most actual problem nowadays. There is a lot of aspects that can be considered in this problem such as the concavity of utility function, market model, the assumptions on the value process, the set of probability measures and the possibility of constructing the optimal investment strategies etc. The main interest in constructing the optimal investment in the very general setup, with an incomplete market, general sets of prior models and non-concave utility functions
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Schedule a callMore From: Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics
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