I am modeling stock exchange according to the present value model as defined by Gregory Chow in this paper. Model operates on natural logarithms of stock prices and dividends in order to "eliminate the effect of the arbitrary number of shares issued". But the companies do not always pay dividends. What should I do when there is a one-year gap in payments? As for now logarithm makes it explode to infinity.
Although this is not something I would favor, sometime when an analyst wants to do a log transformation of a variable Y but Y can take on values greater than or equal to 0, they modify the transformation to be Y=log(X+a) wher a is some small positive constant. Then the minimum value is log(a) rather than negative infinity.