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April 2020 Optimal investment and consumption with labor income in incomplete markets
Oleksii Mostovyi, Mihai Sîrbu
Ann. Appl. Probab. 30(2): 747-787 (April 2020). DOI: 10.1214/19-AAP1514

Abstract

We consider the problem of optimal consumption from labor income and investment in a general incomplete semimartingale market. The economic agent cannot borrow against future income, so the total wealth is required to be positive at (all or some) previous times. Under very general conditions, we show that an optimal consumption and investment plan exists and is unique, and provide a dual characterization in terms of an optional strong supermartingale deflator and a decreasing part, which charges only the times when the no-borrowing constraint is binding. The analysis relies on the infinite-dimensional parametrization of the income/liability streams and, therefore, provides the first-order dependence of the optimal investment and consumption plans on future income/liabilities (as well as a pricing rule).

Citation

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Oleksii Mostovyi. Mihai Sîrbu. "Optimal investment and consumption with labor income in incomplete markets." Ann. Appl. Probab. 30 (2) 747 - 787, April 2020. https://doi.org/10.1214/19-AAP1514

Information

Received: 1 June 2018; Revised: 1 January 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236133
MathSciNet: MR4108121
Digital Object Identifier: 10.1214/19-AAP1514

Subjects:
Primary: 91G10, 93E20
Secondary: 91B16

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 2 • April 2020
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