33 Pages Posted: 23 Apr 2013 Last revised: 24 Oct 2014
Date Written: October 10, 2014
We study the problem of an optimal exit strategy for an investment project which is unprofitable and for which the liquidation costs evolve stochastically. The firm has the option to keep the project going while waiting for a buyer, or liquidating the assets at immediate liquidity and termination costs. The liquidity and termination costs are governed by a mean-reverting stochastic process whereas the rate of arrival of buyers is governed by a regime-shifting Markov process. We formulate this problem as a multidimensional optimal stopping time problem with random maturity. We characterize the objective function as the unique viscosity solution of the associated system of variational Hamilton-Jacobi-Bellman inequalities. We derive explicit solutions and numerical examples in the case of power and logarithmic utility functions when the liquidity premium factor follows a mean-reverting CIR process.
Keywords: real options, stochastic control, liquidity discount, regime shifting, viscosity solutions, system of variational inequalities
JEL Classification: D40, G11
Suggested Citation: Suggested Citation
Chevalier, Etienne and Ly Vath, Vathana and Roch, Alexandre F. and Scotti, Simone, Optimal Exit Strategies for Investment Projects (October 10, 2014). Available at SSRN: https://ssrn.com/abstract=2254973 or http://dx.doi.org/10.2139/ssrn.2254973
By Jim Gatheral