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Time-inconsistent consumption-investment problems in incomplete markets under general discount functions
Yushi Hamaguchi · 2019-12-03 · via math.PR updates on arXiv.org

In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward stochastic differential equation. Moreover, we prove the uniqueness of the open-loop equilibrium pair by showing that the original time-inconsistent problem is equivalent to an associated time-consistent one.

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