02469cam a22002537 4500001000600000003000500006005001700011008004100028100002200069245013700091260006600228490005100294500001400345520143700359530006101796538007201857538003601929700002501965700002401990710004202014830008602056856003702142856003602179t0023NBER20180422085640.0180422s1982 mau||||fs|||| 000 0 eng d1 aBrock, William A.10aStochastic Capital Theory I. Comparative Staticsh[electronic resource] /cWilliam A. Brock, Michael Rothschild, Joseph E. Stiglitz. aCambridge, Mass.bNational Bureau of Economic Researchc1982.1 aNBER technical working paper seriesvno. t0023 aMay 1982.3 aIntroductory lectures on capital theory often begin by analyzing the following problem: I have a tree which will be worth X(t) if cut down at time t. If the discount rate is r, when should the tree be cut down? What is the present value of such a tree? The answers to these questions are straightforward. Since at time t a tree which I plan to cut down at time T is worth e[to the power of rt]e[to the power of ?rT]X(T), I should choose the cutting date T* to maximize e[to the power of -rT]X(T); at t < T* a tree is worth e[to the power of rt]e[to the power of -rT*]X(T*). In this paper we analyze how the answers to these questions of timing and evaluation change when the tree's growth is stochastic rather than deterministic. Suppose a tree will be worth X(t,w) if cut down at time t when X(t,w) is a stochastic process. When should it be cut down? What is its present value? We study these questions for trees which grow according to both discrete and continuous stochastic processes. The approach to continuous time stochastic processes contrasts with much of the finance literature in two respects. First, we obtain sharp aomparative statics results without restricting ourselves to particu,ar stochastic specifications. Second, while the option pricing literature seems to imply that increases in variance always increase value, we show that an increase in the variance of a Tree's growth has ambiguous effects on its value. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aRothschild, Michael.1 aStiglitz, Joseph E.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0023.4 uhttp://www.nber.org/papers/t002341uhttp://dx.doi.org/10.3386/t0023