Optimal timing for an indivisible asset sale

In this paper, we investigate the pricing via utility indifference of the right to sell a non-traded asset. Consider an agent with power utility who owns a single unit of an indivisible, non-traded asset, and who wishes to choose the optimum time to sell this asset. Suppose that this right to sell forms just part of the wealth of the agent, and that other wealth may be invested in a complete frictionless market. We formulate the problem as a mixed stochastic control/optimal stopping problem, which we then solve. We determine the optimal behavior of the agent, including the optimal criteria for the timing of the sale. It turns out that the optimal strategy is to sell the non-traded asset the first time that its value exceeds a certain proportion of the agent's trading wealth. Further, it is possible to characterize this proportion as the solution to a transcendental equation