Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach

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.