Consumption and Investment with Multiple Job-Switching Opportunities
Abstract
We study finite-horizon optimal switching with affine rewards in a consumption-investment model with finitely many occupational regimes. Directed shortest-path costs yield the exact natural borrowing limit. A dual transformation reduces the control problem to a one-dimensional system of variational inequalities with interconnected obstacles. Convexity and a distributional waiting inequality give local spatial C1,1 regularity and smooth fit, including destination ties. These estimates establish strong duality and recover optimal consumption, investment, and switching strategies. A reflected backward stochastic differential equation representation yields a set-based integral formula without prescribed boundary geometry. Every connected component of the spatially regular locus is a maximal smooth graph over time. Exact examples exhibit disconnected contact sets, temporal boundaries under strict triangle costs, and a corner in an individual boundary component under additive route costs. A convergent time discretisation completes the analysis.
Related
- Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem
- Optimal investment and consumption for financial markets with jumps under transaction costs
- Optimal Annuitization, Consumption, and Investment with Costly Capital Injections
- Consumption and Investment When Welfare Floors Change over Time
- Optimal Investment and Consumption in Financial Markets with Integrated Variance Clocks
BibTeX
@misc{ha2026consumption,
title = {{Consumption and Investment with Multiple Job-Switching Opportunities}},
author = {Gugyum Ha and Junkee Jeon},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00900},
eprint = {2611.00900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00900},
}
RIS
TY - UNPB
TI - Consumption and Investment with Multiple Job-Switching Opportunities
AU - Gugyum Ha
AU - Junkee Jeon
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00900
UR - https://arxiv.org/abs/2611.00900
AB - We study finite-horizon optimal switching with affine rewards in a consumption-investment model with finitely many occupational regimes. Directed shortest-path costs yield the exact natural borrowing limit. A dual transformation reduces the control problem to a one-dimensional system of variational inequalities with interconnected obstacles. Convexity and a distributional waiting inequality give local spatial C^1,1 regularity and smooth fit, including destination ties. These estimates establish strong duality and recover optimal consumption, investment, and switching strategies. A reflected backward stochastic differential equation representation yields a set-based integral formula without prescribed boundary geometry. Every connected component of the spatially regular locus is a maximal smooth graph over time. Exact examples exhibit disconnected contact sets, temporal boundaries under strict triangle costs, and a corner in an individual boundary component under additive route costs. A convergent time discretisation completes the analysis.
ER -