Optimal consumption with labor income and borrowing constraints for recursive preferences

Dirk Becherer, Wilfried Kuissi-Kamdem and Olivier Menoukeu-Pamen
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Dirk Becherer: HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
Wilfried Kuissi-Kamdem: Department of Mathematics, University of Rwanda, Kigali 4285, Rwanda
Olivier Menoukeu-Pamen: University of Liverpool

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Abstract: We study the optimal consumption and investment problem for an investor with liquidity constraints who has isoelastic recursive Epstein-Zin utility preferences and receives a stochastic stream of income. We characterize the optimal consumption strategy as well as the terminal wealth for recursive utility under dynamic liquidity constraints, which prevent the investor to borrow against his stochastic future income. Using duality and backward SDE methods in a possibly non-Markovian diffusion model for the financial market, this gives rise to an interplay of singular control and optimal stopping problems. Our analysis extends to more general liquidity constraints.

Keywords: Liquidity constraints; Optimal consumption; Stochastic income; Epstein-Zin recursive utility; Duality; Optimal stopping; Singular control; Reflected BSDE (search for similar items in EconPapers)
Date: 2023-03-07
New Economics Papers: this item is included in nep-upt
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