Optimal Timing for an Asset Sale in an Incomplete Market

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 can be invested in a complete frictionless market. We express the problem as a mixed stochastic control/optimal stopping problem. We analyse the problem of determining the optimal behaviour of the agent, including the optimal criteria for the timing of the sale. It turns out that the Department of Mathematical Sciences, University of Bath, Bath. BA2 7AY. UK. Email: [email protected] Bendheim Center for Finance and ORFE, Princeton University, Princeton, NJ, 08544. USA. Email: [email protected]. The second author is partially supported by the NSF under grant DMI 0447990. Department of Mathematical Sciences, University of Bath, Bath. BA2 7AY. UK, and ORFE, Princeton University, Princeton, NJ, 08544. USA. Email: [email protected]. The third author is supported by an Epsrc Advanced Fellowship.