Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach
Abstract
We study a two-sided singular stochastic control problem in which changes in consumption carry utility costs and the risk premium follows the mean-reverting Kim-Omberg model. Optimal consumption is reflected between two moving barriers given by thresholds that depend on the current risk premium. These thresholds are the stopping boundaries of a Dynkin game for a two-dimensional diffusion driven by a single Brownian motion. A sharp occupation estimate shows that they are Lipschitz in logarithmic scale, uniformly in the cost of reducing consumption, and that smooth fit holds along the diffusion direction at every contact point. Outside a bounded interval of risk premia and at most two further points, the thresholds are infinitely differentiable. As the reduction cost grows, optimal consumption converges to the ratcheting policy.
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BibTeX
@misc{ha2026consumption,
title = {{Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach}},
author = {Gugyum Ha and Junkee Jeon and Jehan Oh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14524},
eprint = {2610.14524},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14524},
}
RIS
TY - UNPB
TI - Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach
AU - Gugyum Ha
AU - Junkee Jeon
AU - Jehan Oh
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14524
UR - https://arxiv.org/abs/2610.14524
AB - We study a two-sided singular stochastic control problem in which changes in consumption carry utility costs and the risk premium follows the mean-reverting Kim-Omberg model. Optimal consumption is reflected between two moving barriers given by thresholds that depend on the current risk premium. These thresholds are the stopping boundaries of a Dynkin game for a two-dimensional diffusion driven by a single Brownian motion. A sharp occupation estimate shows that they are Lipschitz in logarithmic scale, uniformly in the cost of reducing consumption, and that smooth fit holds along the diffusion direction at every contact point. Outside a bounded interval of risk premia and at most two further points, the thresholds are infinitely differentiable. As the reduction cost grows, optimal consumption converges to the ratcheting policy.
ER -