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Irreversible capital accumulation under interest rate uncertainty

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Abstract

We consider the optimal sequential irreversible investment policy of a value maximizing firm facing decreasing returns to scale and interest rate uncertainty. We characterize the optimal accumulation policy and its value for a broad class of diffusion models of the short interest rate by focusing on the marginal investment decision and deriving the marginal value of capital explicitly. We also state a set of conditions under which there is a maximal capital stock above which the option to expand productive capacity further in the future becomes valueless. Hence, our results indicate that interest rate uncertainty may limit the size of an optimally investing firm.

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References

  • Abel AB (1990) Consumption and investment. In: Friedman F, Hahn F (eds) Handbook of monetary economics, vol II. North-Holland, New York, pp 725–778

    Google Scholar 

  • Abel AB, Eberly JC (1996) Optimal investment with costly reversibility. Rev Econ Stud 63: 581–593

    Article  MATH  Google Scholar 

  • Abel AB, Eberly JC (1999) The effects of irreversibility and uncertainty on capital accumulation. J Monetary Econ 44: 339–377

    Article  Google Scholar 

  • Abel AB, Dixit AK, Eberly JC, Pindyck RS (1996) Options, the value of capital, and investment. Q J Econ 111: 753–777

    Article  MATH  Google Scholar 

  • Abramowitz, M, Stegun, IA (eds) (1968) Handbook of mathematical functions. Dover Publications, New York

    Google Scholar 

  • Alvarez LHR (2003) On the convexity and risk-sensitivity of the price of American interest rate derivatives. SIAM J Appl Math 63: 923–936

    Article  MATH  MathSciNet  Google Scholar 

  • Alvarez LHR, Koskela E (2003) On forest rotation under interest rate variability. Int Tax Public Financ 10: 489–503

    Article  Google Scholar 

  • Alvarez LHR, Koskela E (2005) Wicksellian theory of forest rotation under interest rate variability. J Econ Dyn Control 29: 529–545

    Article  MATH  MathSciNet  Google Scholar 

  • Alvarez LHR, Koskela E (2006) Irreversible investment under interest rate variability: some generalizations. J Bus 79: 623–644

    Article  Google Scholar 

  • Arrow KJ (1968) Optimal capital policy with irreversible investment. In: Wolfe JN (ed) Value, capital and growth: papers in honour of sir John Hicks, Chicago, pp 1–19

  • Baldursson FM, Karatzas I (1997) Irreversible investment and industry equilibrium. Financ Stochast 1: 69–89

    Article  MATH  Google Scholar 

  • Baldwin C (1982) Optimal sequential investment when capital is not readily reversible. J Financ 37: 763–782

    Article  Google Scholar 

  • Bather J, Chernoff H (1966) Sequential decisions in the control of a spaceship. Proc Fifth Berkeley Symp Math Stat Prob 3: 181–207

    Google Scholar 

  • Bertola G (1998) Irreversible investment. Res Econ 52: 3–37

    Article  MATH  Google Scholar 

  • Borodin A, Salminen P (2002) Handbook on Brownian motion—facts and formulae, 2nd edn. Birkhauser, Basel

    Google Scholar 

  • Caballero RJ (1999) Aggregate investment. In: Taylor JP, Woodford M (eds) Handbook of macroeconomics, Vol. 1B, pp 813–862

  • Caballero RJ, Leahy JV (1996) Fixed costs: the demise of marginal q. NBER working paper No. 5508

  • Chow PL, Menaldi J-L, Robin M (1985) Additive control of stochastic linear systems with finite horizon. SIAM J Control Optim 23: 858–899

    Article  MATH  MathSciNet  Google Scholar 

  • Cooper R, Ejarque J (2003) Financial frictions and investment: requiem in Q. Rev Econ Dyn 6: 710–728

    Article  Google Scholar 

  • Cox JC, Ingersoll JE, Ross SA (1980) An analysis of variable rate loan contracts. J Financ 35: 389–403

    Article  Google Scholar 

  • Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53: 385–407

    Article  MathSciNet  Google Scholar 

  • Davis MHA, Zervos M (1994) A problem of singular stochastic control with discretionary stopping. Ann Appl Prob 4: 226–240

    Article  MATH  MathSciNet  Google Scholar 

  • Davis MHA, Zervos M (1998) A pair of explicitly solvable singular stochastic control problems. Appl Math Optim 38: 327–352

    Article  MATH  MathSciNet  Google Scholar 

  • Dixit AK (1995) Irrversible investment with uncertainty and scale economies. J Econ Dyn Control 19: 327–350

    Article  MATH  Google Scholar 

  • Dixit AK, Pindyck RS (1994) Investment under uncertainty. Princeton UP, Princeton

    Google Scholar 

  • Harrison JM, Taksar MI (1983) Instantaneous control of Brownian motion. Math Oper Res 8: 439–453

    Article  MATH  MathSciNet  Google Scholar 

  • Hayashi F (1982) Tobin’s marginal q and average q: a neoclassical interpretation. Econometrica 50: 213–224

    Article  MATH  Google Scholar 

  • Ingersoll JE Jr, Ross SA (1992) Waiting to invest: investment and uncertainty. J Bus 65: 1–29

    Article  Google Scholar 

  • Jorgenson D (1963) Capital theory and investment behavior. Am Econ Rev 53: 247–259

    Google Scholar 

  • Karatzas I (1983) A class of singular stochastic control problems. Adv Appl Prob 15: 225–254

    Article  MathSciNet  Google Scholar 

  • Karatzas I, Shreve SE (1985) Connections between optimal stopping and singular stochastic control II. Reflected follower problems. SIAM J Control Optim 23: 433–451

    Article  MATH  MathSciNet  Google Scholar 

  • Karatzas I, Shreve S (1991) Brownian motion and stochastic calculus. Springer, New York

    MATH  Google Scholar 

  • Karlin S, Taylor H (1981) A second course in stochastic processes. Academic Press, Orlando

    MATH  Google Scholar 

  • Kobila TØ (1993) A class of solvable stochastic investment problems involving singular controls. Stochast Stochast Reports 43: 29–63

    MATH  MathSciNet  Google Scholar 

  • Merton RC (1975) An asymptotic theory of growth under uncertainty. Rev Econ Stud 42: 375–393

    Article  Google Scholar 

  • Nickell SJ (1974) On the role of expectations in the pure theory of investment. Rev Econ Stud 41: 1–19

    Article  MATH  Google Scholar 

  • Nickell SJ (1974) On expectations, government policy and the rate of investment. Economica 41: 241–255

    Article  Google Scholar 

  • Nickell SJ (1978) The investment decisions of firms. Cambridge UP, Oxford

    Google Scholar 

  • Øksendal A (2000) Irreversible investment problems. Financ Stochast 4: 223–250

    Article  Google Scholar 

  • Øksendal B (2003) Stochastic differential equations: an introduction with applications, 6th edn. Springer, Berlin

    Google Scholar 

  • Pindyck RS (1988) Irreversible investment, capacity choice, and the value of the firm. Am Econ Rev 78: 969–985

    Google Scholar 

  • Pindyck RS (1991) Irreversibility, uncertainty, and investment. J Econ Lit 29: 1110–1152

    Google Scholar 

  • Protter P (2004) Stochastic integration and differential equations, 2nd edn. Springer, New York

    MATH  Google Scholar 

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Correspondence to Luis H. R. Alvarez.

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Alvarez, L.H.R. Irreversible capital accumulation under interest rate uncertainty. Math Meth Oper Res 72, 249–271 (2010). https://doi.org/10.1007/s00186-010-0319-0

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  • DOI: https://doi.org/10.1007/s00186-010-0319-0

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