We study a continuous-time model of consumption and portfolio selection of an agent with a limited ability to commit to a debt contract in which the credit limit is endogenously determined. We consider the case where the agent borrows against future income and/or collateral assets. We also study the determination of the credit limit in a general equilibrium model. We derive the credit limit in closed form. The credit limit is smaller than the natural limit because of limited commitment and an increasing function of both income and the collateral price. We extend the baseline model to the case with a regime switch and show that the credit limit is cyclical; it is lower (higher) when the Sharpe ratio is high (low). The model predicts that the rich tend to increase the proportion of risky investments in downturns, whereas the poor decrease them.
H. K. Koo acknowledges the support by the National Research Foundation of Korea grant funded by the Korean Government [NRF-2020R1A2C1A01006134, NRF-2021S1A5A2A03065678], and B. H. Lim acknowledges support by the National Research Foundation of Korea grant funded by the Korean Government (NRF-2020R1F1A1A01076116). The authors thank Hengjie Ai, Michael Brennan, Alex David, Philip Dybvig, Dirk Krueger, Mark Loewenstein, Emilio Osambela, Neng Wang, Junkee Jeon, and the participants at the 2019 North American Summer Meeting of the Econometric Society, the 2017 Society for Advanced Economic Theory Conference; the 2016 Meeting of Japanese Association of Financial Econometrics and Engineering; the 2016 Asian Meeting of Econometric Society; the 2016 Bachelier Finance Congress; the 2015 Workshop at the Institute for Financial Studies; Southwest University of Finance and Economics (SWUFE); and the 2014 Northern Finance Association meeting for their helpful comments and discussions on the current and previous versions of this paper. The authors also thank the area editor, the associate editor, and anonymous referees for valuable comments.
