Optimal investment and consumption in a continuous-time co-integration model

This paper discusses an optimal investment-consumption problem in a continuous-time co-integration model, where an investor aims to maximize an expected, discounted utility derived from intertemporal consumption and terminal wealth in a finite time horizon. Using the dynamic programming principle approach, we obtain an Hamilton-Jacobi-Bellman equation related to the problem. In each of the power and logarithmic utility cases, we obtain semi-closed-form expressions of the investment-consumption strategy and the value function. We also provide some numerical examples to illustrate these theoretical results.