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Stochastic Capital Theory

  • 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)
To distinguish from intrinsic value, call this latter quantity the market value of the asset.

Keywords

Interest Rate Discount Rate Free Boundary Local Increase Geometric Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© George R. Feiwel 1989

Authors and Affiliations

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

There are no affiliations available

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