Publikation: Portfolio Optimization under Nonlinear Utility
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2016
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International Journal of Theoretical and Applied Finance. 2016, 19(5), 1650029. ISSN 0219-0249. eISSN 1793-6322. Available under: doi: 10.1142/S0219024916500291
Zusammenfassung
This paper studies the utility maximization problem of an agent with non-trivial endowment, and whose preferences are modeled by the maximal subsolution of a BSDE. We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled FBSDE. Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.
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Fachgebiet (DDC)
510 Mathematik
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Subsolutions of BSDEs; submartingale; convex duality; utility maximization
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HEYNE, Gregor, Michael KUPPER, Ludovic TANGPI, 2016. Portfolio Optimization under Nonlinear Utility. In: International Journal of Theoretical and Applied Finance. 2016, 19(5), 1650029. ISSN 0219-0249. eISSN 1793-6322. Available under: doi: 10.1142/S0219024916500291BibTex
@article{Heyne2016Portf-30887.2,
year={2016},
doi={10.1142/S0219024916500291},
title={Portfolio Optimization under Nonlinear Utility},
number={5},
volume={19},
issn={0219-0249},
journal={International Journal of Theoretical and Applied Finance},
author={Heyne, Gregor and Kupper, Michael and Tangpi, Ludovic},
note={Article Number: 1650029}
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<dcterms:abstract xml:lang="eng">This paper studies the utility maximization problem of an agent with non-trivial endowment, and whose preferences are modeled by the maximal subsolution of a BSDE. We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled FBSDE. Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.</dcterms:abstract>
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