Horizon-unbiased utility functions

In this paper we consider a class of mixed optimal control/optimal stopping problems related to the choice of the best time to sell a single unit of an indivisible asset. We assume that in addition to the indivisible asset, the agent has access to a financial market. Investments in the financial market can be used for hedging, but the financial assets are only partially correlated with the indivisible asset, so that the agent faces an incomplete markets problem.We show how, even in the infinite horizon case, it is possible to express the problem as a maximisation problem with respect to an inter-temporal utility function evaluated at the sale time, but that this objective function must satisfy consistency conditions over time.