I am trying to understand geometric Brownian motion as it relates to the present discounted value of future dividend payments.
I am supposing that a company has a revenue stream $f(t)$. This is just $profits-expenditures$ at time $t$.
The revenue stream is upwards sloping, one reason being that the company usually invests profits back into itself. At some point in time, the marginal benefit of reinvesting $\\\$1$ back into the company is less than returning the $\\\$1$ back to shareholders in the form of dividend payments.
How does the company decide when it is time to make dividend payments? Are there mathematical models for this decision? Are there books on this subject?
