Optimal investment and consumption with labor income in incomplete markets
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 martingale deflators and decreasing parts, which allow for a limit that 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). An emphasis is placed on mathematical generality.
Keywords
Cite
@article{arxiv.1806.05901,
title = {Optimal investment and consumption with labor income in incomplete markets},
author = {Oleksii Mostovyi and Mihai Sîrbu},
journal= {arXiv preprint arXiv:1806.05901},
year = {2019}
}
Comments
45 pages. In this version, we present an exact (rather than approximate) complementary slackness characterization in section 6, by giving an explicit structure of the dual minimizer in Theorem 6.1. We also have expanded the literature review