# Time-Inconsistent Consumption-Investment Problems in Incomplete Markets under General Discount Functions

@article{Hamaguchi2021TimeInconsistentCP, title={Time-Inconsistent Consumption-Investment Problems in Incomplete Markets under General Discount Functions}, author={Yushi Hamaguchi}, journal={SIAM J. Control. Optim.}, year={2021}, volume={59}, pages={2121-2146} }

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…

## 4 Citations

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