BFS 2002 

Contributed Talk 
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 BSDEvariant of Skorohod's obstacle problem. The solution of this problem is obtained via a representation theorem for optional processes which characterizes the timevarying 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.
wws.mathematik.huberlin.de/~pbank