PORTFOLIO OPTIMIZATION UNDER NONLINEAR UTILITY

Gregor Heyne (), Michael Kupper () and Ludovic Tangpi ()
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Gregor Heyne: Department of Mathematics, Humboldt University of Berlin, Unter den Linden 6 – 10099 Berlin, Germany
Michael Kupper: Department Mathematics and Statistics, Universität Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany
Ludovic Tangpi: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 05, 1-37

Abstract: This paper studies the utility maximization problem of an agent with nontrivial endowment, and whose preferences are modeled by the maximal subsolution of a backward stochastic differential equation (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 forward–BSDE (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.

Keywords: Subsolutions of BSDEs; submartingale; convex duality; utility maximization (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024916500291

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