Optimal capital accumulation under price uncertainty and costly reversibility

We consider the optimal capital accumulation policy of a competitive firm operating in the presence of decreasing returns to scale, price uncertainty, and costly reversibility of investment. We characterize the optimal accumulation policy and derive the value of the firm by focusing on the marginal investment decision and solving the associated optimal timing problem characterizing the option value of the associated opportunity to either disinvest or acquire a marginal unit of capacity. We also characterize the required exercise premia associated with the optimal policies and demonstrate that hysteresis prevails within this class of accumulation problems as well.

[1]  Avinash Dixit,et al.  Options, the Value of Capital, and Investment , 1995 .

[2]  M. Shackleton,et al.  Harvesting and recovery decisions under uncertainty , 2010 .

[3]  José Carlos Dias,et al.  Hysteresis Effects Under CIR Interest Rates , 2010, Eur. J. Oper. Res..

[4]  S. Shreve,et al.  Connections Between Optimal Stopping and Singular Stochastic Control II. Reflected Follower Problems , 1985 .

[5]  Anders Øksendal,et al.  Irreversible investment problems , 2000, Finance Stochastics.

[6]  A. Shiryaev,et al.  Hiring and firing optimally in a large corporation , 1996 .

[7]  Janice C. Eberly,et al.  Optimal Investment with Costly Reversibility , 1996 .

[8]  Eduardo S. Schwartz,et al.  Evaluating Natural Resource Investments , 1985 .

[9]  Ricardo J. Caballero,et al.  Fixed Costs: The Demise of Marginal Q , 1996 .

[10]  Fumio Hayashi,et al.  TOBIN'S MARGINAL q AND AVERAGE q: A NEOCLASSICAL INTERPRETATION , 1982 .

[11]  A. Dixit.  Entry and Exit Decisions under Uncertainty , 1989, Journal of Political Economy.

[12]  Sudipto Sarkar,et al.  On the investment-uncertainty relationship in a real options model , 2000 .

[13]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[14]  Ioannis Karatzas,et al.  Irreversible investment and industry equilibrium , 1996, Finance Stochastics.

[15]  K. Arrow.  OPTIMAL CAPITAL POLICY WITH IRREVERSIBLE INVESTMENT , 1966 .

[16]  Stephen Nickell,et al.  On the Role of Expectations in the Pure Theory of Investment Review of Economic Studies , 1974 .

[17]  K. Wong.  The effect of uncertainty on investment timing in a real options model , 2007 .

[18]  Janice C. Eberly,et al.  The Effects of Irreversibility and Uncertainty on Capital Accumulation , 1999 .

[19]  Stephen Nickell,et al.  On Expectations, Government Policy and the Rate of Investment , 1974 .

[20]  R. Pindyck.  Irreversibility, Uncertainty, and Investment , 1990 .

[21]  J. Hicks,et al.  Value, capital, and growth;: Papers in honour of Sir John Hicks , 1968 .

[22]  Giuseppe Bertola,et al.  Firing Costs and Labour Demand: How Bad is Eurosclerosis? , 1990 .

[23]  Ricardo J. Caballero,et al.  Irreversibility and Aggregate Investment , 1991 .

[24]  Sigbjørn Sødal.  Entry and exit decisions based on a discount factor approach , 2006 .

[25]  M. Shackleton,et al.  Smooth Pasting as Rate of Return Equalization , 2005 .

[26]  S. Karlin,et al.  A second course in stochastic processes , 1981 .

[27]  John Leahy.  Investment in Competitive Equilibrium: The Optimality of Myopic Behavior , 1993 .

[28]  Fridrik M. Baldursson,et al.  Irreversible investment under uncertainty in oligopoly , 1998 .

[29]  Ricardo J. Caballero.  Chapter 12 Aggregate investment , 1999 .

[30]  Andrew B. Abel,et al.  Consumption and Investment , 1988 .

[31]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[32]  Avinash Dixit,et al.  Irreversible Investment with Uncertainty and Scale Economies , 1992 .

[33]  S. Nickell.  The investment decisions of firms , 1979 .

[34]  Finite Maturity Caps and Floors on Continuous Flows , 2007 .

[35]  T. Kobila.  A Class of Solvable Stochastic Investment Problems Involving Singular Controls , 1993 .

[36]  J. Harrison,et al.  Brownian motion and stochastic flow systems , 1986 .

[37]  L. Alvarez,et al.  A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation , 2006 .

[38]  Carliss Y. Baldwin.  Optimal Sequential Investment When Capital is Not Readily Reversible , 1982 .

[39]  Avinash Dixit,et al.  Investment and Hysteresis , 1992 .

[40]  Frank Riedel,et al.  On Irreversible Investment , 2006 .