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February 2019 Exponential utility maximization under model uncertainty for unbounded endowments
Daniel Bartl
Ann. Appl. Probab. 29(1): 577-612 (February 2019). DOI: 10.1214/18-AAP1428

Abstract

We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options.

We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further, it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed.

Citation

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Daniel Bartl. "Exponential utility maximization under model uncertainty for unbounded endowments." Ann. Appl. Probab. 29 (1) 577 - 612, February 2019. https://doi.org/10.1214/18-AAP1428

Information

Received: 1 June 2017; Revised: 1 January 2018; Published: February 2019
First available in Project Euclid: 5 December 2018

zbMATH: 07039133
MathSciNet: MR3910012
Digital Object Identifier: 10.1214/18-AAP1428

Subjects:
Primary: 49L20, 91B16
Secondary: 60G42

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2019
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