  We propose a model in which dividend payments occur at regular, deterministic
intervals in an otherwise continuous model. This contrasts traditional models
where either the payment of continuous dividends is controlled or the dynamics
are given by discrete time processes. Moreover, between two dividend payments,
the structure allows for other types of control; we consider the possibility of
equity issuance at any point in time. The value is characterized as the fixed
point of an optimal control problem with periodic initial and terminal
conditions. We prove the regularity and uniqueness of the corresponding dynamic
programming equation, and the convergence of an efficient numerical algorithm
that we use to study the problem. The model enables us to find the loss caused
by infrequent dividend payments. We show that under realistic parameter values
this loss varies from around 1% to 24% depending on the state of the system,
and that using the optimal policy from the continuous problem further increases
the loss.
