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how much the lack of stationarity would affect the estimates of the crucial parameters of the theory. From equation 9 , y can be seen to depend only upon the ratios i d2 and 6 c2, and hence one might expect from the results in Tlla that the estimates of y for the Allegheny series would be robust for different interval lengths. .For the same reasons, the estimates for Atlas and Tri-Continental would be expected to vary considerably. There are three reasonable alternative hypotheses to the simple...
Analytical Optimal Control Theory As Applied To Stochastic And Nonstochastic
ROBERT COX MERTON .S., Columbia School of Engineering amp Applied Science M.S., California Institute of Technology SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS' FOR THE DEGREE OF DOCTOR QF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September, 1970 ignature of Author Department of Economics, August 28, 1970 ertified by t _ Chairman, Departmental Committee on Graduate Students
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Where there is no risk-free asset, it is assumed no asset can be expressed as a linear combination of the other assets, implying th t the nxn variance-covariance matrix of returns, n - c where cr p a. a., is non-singular. In the caseJ when thereJ is a1'1 1 J risk-free asset, the same assumption is made about the reduced mxrn variance-covariance matrix. V is short for the rigorous D , the Dynkin operator over the variables P and W for a given set of controls
An Empirical Investigation Of The Samuelson Rational Warrant Pricing Theory
Optimum Consumption and Portfolio Rules In a Corit'inuous-t'lme Model Robert C. Merton M.I.T. March , 1970 1. Introduction. A common hypothesis about the behavior of limited liability asset prices in perfect markets is the random walk of returns or in its continuous-time form the geometric Brownian motion hypothesis which implies that asset prices are stationary and log-normally distributed, A number of investigators of the behavior of stock and commodity prices have questioned the accuracy of...