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Divergence between sample path and moments behavior: An issue in the application of geometric brownian motion to finance
Date Issued
1994
ISSN
0736-2994
1532-9356
Citation
Stochastic Analysis and Applications, 1994, vol. 12(3), pp. 277-290.
Type
Peer Reviewed Journal Article
Abstract
Geometric Brownian motion is one of the most frequently used tools in modelling stock prices. To complete the general equilibrium analysis, the expected rate of return on each stock is usually assumed to be equal to the risk-free rate of interest. However, there is a divergence between the moments and sample path behavior of the stock price process. A stock with an exponentially increasing expected value and a positive expected rate of return may have a typical sample path which approaches 0 asymptotically, so that a serious problem arises in the interpretation of asset markets equilibrium. We suggest that by introducing risk adjustment, it is possible to overcome this problem
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