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Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

Deng, Shuoqing ; Tan, Xiaolu ; Yu, Xiang

Mathematics of operations research, 2020-11, Vol.45 (4), p.1210-1236 [Periódico revisado por pares]

Linthicum: INFORMS

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Título:
Utility Maximization with Proportional Transaction Costs Under Model Uncertainty
Autor: Deng, Shuoqing ; Tan, Xiaolu ; Yu, Xiang
Assuntos: Analysis ; convex duality ; Costs ; Duality theorem ; Duality theory (Mathematics) ; Dynamic programming ; Economic aspects ; Endowment ; Endowments ; Existence theorems ; Financial markets ; Investment analysis ; Mathematical optimization ; Mathematical research ; Maximization ; model uncertainty ; Operations research ; Optimization ; Primary: 60G42, 49M29 ; Primary: Probability/stochastic model applications ; Profit maximization ; randomization method ; secondary: 49L20, 91B16 ; secondary: finance/asset pricing ; Securities markets ; Transaction costs ; Uncertainty ; utility indifference pricing ; utility maximization
É parte de: Mathematics of operations research, 2020-11, Vol.45 (4), p.1210-1236
Descrição: 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.
Editor: Linthicum: INFORMS
Idioma: Inglês

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Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

Deng, Shuoqing ; Tan, Xiaolu ; Yu, Xiang

Linthicum: INFORMS

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