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Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization

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  • Samuel Drapeau
  • Peng Luo
  • Dewen Xiong

Abstract

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with explicit examples how to quantify the costs of incompleteness when using utility indifference pricing, as well as a way to find optimal solutions for recursive utilities.

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  • Samuel Drapeau & Peng Luo & Dewen Xiong, 2017. "Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization," Papers 1703.02694, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1703.02694
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    References listed on IDEAS

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    6. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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    8. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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