# Dividend as a function of stock

Let's say I have a stock that pays dividend once a year. I know how much did it pay in 2014, and at which level was stock trading when the dividend decision was made. I'd like to use these data to estimate dividend of 2015 as a function of the stock price: $D = f(S)$. Clearly, $f(S) \leq S$ and a naive assumption would be that $f$ is monotonic. Is there any research done on this topic, I mean what are other natural properties $f$ shall have, and examples of it?