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Viscosity properties with singularities in a state-constrained expected utility maximization problem

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  • Mourad Lazgham

Abstract

We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough). On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation.

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  • Mourad Lazgham, 2015. "Viscosity properties with singularities in a state-constrained expected utility maximization problem," Papers 1510.03584, arXiv.org.
    • Handle: RePEc:arx:papers:1510.03584
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    References listed on IDEAS

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    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    3. Mourad Lazgham, 2015. "Regularity properties in a state-constrained expected utility maximization problem," Papers 1510.03079, arXiv.org.
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