scholarly journals Robust Utility Maximization Under Model Uncertainty via a Penalization Approach

2020 ◽  
Author(s):  
Ivan Guo ◽  
Nicolas Langrené ◽  
Gregoire Loeper ◽  
Wei Ning
Keyword(s):  
Model Uncertainty ◽  
Utility Maximization ◽  
Robust Utility Maximization

scholarly journals Duality theory under model uncertainty for non-concave utility functions

2019 ◽  
pp. 50-56
Author(s):  
O. O. Kharytonova
Keyword(s):  
Probabilistic Model ◽  
Model Uncertainty ◽  
Duality Theory ◽  
Utility Maximization ◽  
Utility Functions ◽  
Previous Literature ◽  
Market Models ◽  
Terminal Wealth ◽  
Complete Market ◽  
Robust Utility Maximization

The main goal for this paper is to study the robust utility maximization functional, i.e. sup_{X\in\Xi(x)} inf_{Q\in\mathsf{Q}} E_Q [U(X_T)]; of the terminal wealth in complete market models, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In the previous literature, this problem was studied for strictly concave utility functions and we extended existing results for non-concave utility functions by considering their concavization.

scholarly journals Robust Utility Maximization without Model Compactness

2016 ◽  
Vol 7 (1) ◽  
pp. 70-103 ◽  
Author(s):  
Julio D. Backhoff Veraguas ◽  
Joaquín Fontbona
Keyword(s):  
Utility Maximization ◽  
Robust Utility Maximization

scholarly journals Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

2020 ◽  
Vol 45 (4) ◽  
pp. 1210-1236 ◽  
Author(s):  
Shuoqing Deng ◽  
Xiaolu Tan ◽  
Xiang Yu
Keyword(s):  
Dynamic Programming ◽  
Transaction Costs ◽  
Model Uncertainty ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Market Condition ◽  
Maximization Problem ◽  
Proportional Transaction Costs ◽  
Utility Indifference ◽  
Basic Features

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.

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