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Stochastic Capital Theory

In: Joan Robinson and Modern Economic Theory

Author

Listed:
  • William A. Brock
  • Michael Rothschild
  • Joseph E. Stiglitz

Abstract

Many problems in capital theory — particularly ‘Austrian’ capital theory —take the following form: an asset has an intrinsic value X(t) at time t. If he takes a particular action at time T, then the asset’s owner gets X(T) at T. In anticipation of future usage we shall call the action taken at T stopping and refer to T as a stopping time. This set-up raises two natural, and related, questions. When should the intrinsic process be stopped? What is the present value of the asset? The standard examples are when to drink the wine whose quality at t is given by X(t) or when to cut down the tree which contains lumber with a value of X(t). If the discount rate is r then these questions may be simply answered. The optimal stopping time T* maximizes e -rT X(T) and the present value of the tree is its discounted value 1 V ( t ) = e − r ( T * − t ) X ( T * ) ]]

Suggested Citation

  • William A. Brock & Michael Rothschild & Joseph E. Stiglitz, 1989. "Stochastic Capital Theory," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Joan Robinson and Modern Economic Theory, chapter 20, pages 591-622, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-349-08633-7_20
    DOI: 10.1007/978-1-349-08633-7_20
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    Citations

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    Cited by:

    1. Fernandez, Linda & Karp, Larry, 1994. "Wetlands Mitigation Banks: A Developer's Investment Problem," CUDARE Working Papers 201376, University of California, Berkeley, Department of Agricultural and Resource Economics.
    2. Davis, Graham A. & Cairns, Robert D., 2012. "Good timing: The economics of optimal stopping," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 255-265.
    3. Chang, Fwu-Ranq, 2005. "On the elasticities of harvesting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 469-485, March.
    4. Meyer, Elisabeth & Rees, Ray, 2012. "Watchfully waiting: Medical intervention as an optimal investment decision," Journal of Health Economics, Elsevier, vol. 31(2), pages 349-358.
    5. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1121-1141.
    6. Baudry, Marc, 1999. "Stock externalities and the diffusion of less polluting capital: an option approach," Structural Change and Economic Dynamics, Elsevier, vol. 10(3-4), pages 395-420, December.
    7. Linda Fernandez & Larry Karp, 1998. "Restoring Wetlands Through Wetlands Mitigation Banks," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 12(3), pages 323-344, October.
    8. Marc Baudry, 2000. "Joint Management of Emission Abatement and Technological Innovation for Stock Externalities," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 16(2), pages 161-183, June.
    9. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    10. Minh Ha-Duong & Benoit Morel, 2003. "The real option with an absorbing barrier," Post-Print halshs-00003976, HAL.

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