BFS 2002

Contributed Talk

Optimal consumption rules in the presence of durable and perishable goods

Peter Bank, Nicole El Karoui, Frank Riedel

We discuss the utility maximization problem of an economic agent who obtains utility both from a perishable and a durable good. Introducing the gradient approach to this mixed classical/singular control problem, we show how the first order conditions for optimality reduce to a BSDE-variant of Skorohod's obstacle problem. The solution of this problem is obtained via a representation theorem for optional processes which characterizes the time--varying minimal storage level of durable goods to be held at each point in time. We explain how to derive this process from the given price and preference structure and provide some explicit solutions. We close by presenting an efficent and easily implementable algorithm which allows one to compute the minimal storage level process in a discrete time setting.