Optimal Exit Strategies for Investment Projects

33 Pages Posted: 23 Apr 2013 Last revised: 24 Oct 2014

Etienne Chevalier

Université de Marne-la-Vallée

Vathana Ly Vath

Université d'Évry

Alexandre F. Roch

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG)

Simone Scotti

Université Paris VII Denis Diderot

Date Written: October 10, 2014

Abstract

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

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

Etienne Chevalier

Université de Marne-la-Vallée ( email )

6-8 Cours du Danube
5, Bd Descartes
Serris, Marne-la-Vallée Cedex 2 77700
France

Vathana Ly Vath

Université d'Évry ( email )

Bd. François Mitterrand
F-91025 Evry Cedex, 91028
France

Alexandre F. Roch (Contact Author)

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG) ( email )

Case postale 8888
Succursale Centre-ville
Montreal, Quebec H3C 3P8
Canada

Simone Scotti

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

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