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arXiv · 1510.03584

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

Mourad Lazgham
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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. 2015-10-13. Viscosity properties with singularities in a state-constrained expected utility maximization problem. https://arxiv.org/abs/1510.03584

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