|Date: Wednesday, December 11, 2019
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: Optimal Consumption under Habit Formation Constraints
Abstract: I will present two models of optimal consumption under a constraint that prevents the agent's consumption to fall below a certain proportion of her current "consumption habit." In the first model, consumption habit is the running maximum of past consumption, while the second model assumes that habit is the exponentially weighted moving average of past consumption. For each case, a stochastic control problem is formulated with the objective of maximizing the expected discounted utility of consumption stream while investing in a Black-Scholes financial market. The resulting Hamilton-Jacobi-Bellman equations are reduced to non-linear free-boundary problems that are subsequently solved semi-explicitly. The optimal consumption policy in the two models share common features in that they are mainly driven by the wealth-to-habit ratio. Furthermore, there are critical values of the wealth-to-habit ratio that determines when it is optimal to consume at the minimum acceptable rate, when should the consumption rate be above the minimum, and when is it optimal to raise the consumption habit above its current value.
The talk is based on joint work with Erhan Bayraktar and Virginia Young.
Speaker: Bahman Angoshtari
Institution: University of Washington