## The Annals of Applied Probability

### Exponential utility maximization under model uncertainty for unbounded endowments

Daniel Bartl

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 29, Number 1 (2019), 577-612.

Dates
Revised: January 2018
First available in Project Euclid: 5 December 2018

https://projecteuclid.org/euclid.aoap/1544000437

Digital Object Identifier
doi:10.1214/18-AAP1428

Mathematical Reviews number (MathSciNet)
MR3910012

Zentralblatt MATH identifier
07039133

Subjects
Primary: 91B16: Utility theory 49L20: Dynamic programming method
Secondary: 60G42: Martingales with discrete parameter

#### Citation

Bartl, Daniel. Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29 (2019), no. 1, 577--612. doi:10.1214/18-AAP1428. https://projecteuclid.org/euclid.aoap/1544000437

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