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}
}
  • Yushi Hamaguchi
  • Published 3 December 2019
  • Economics, Mathematics
  • SIAM J. Control. Optim.
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… 
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