  In this paper we study a class of optimal dividend and investment problems
assuming that the underlying reserve process follows the Sparre Andersen model,
that is, the claim frequency is a "renewal" process, rather than a standard
compound Poisson process. The main feature of such problems is that the
underlying reserve dynamics, even in its simplest form, is no longer Markovian.
By using the backward Markovization technique we recast the problem in a
Markovian framework with expanded dimension representing the time elapsed after
the last claim, with which we investigate the regularity of the value function,
and validate the dynamic programming principle. Furthermore, we show that the
value function is the unique constrained viscosity solution} to the associated
HJB equation on a cylindrical domain on which the problem is well-defined.
