  The discrete sell or hold problem (DSHP), which is introduced in \cite{H12},
is studied under the constraint that each asset can only take a constant number
of different values. We show that if each asset can take only two values, the
problem becomes polynomial-time solvable. However, even if each asset can take
three different values, DSHP is still NP-hard. An approximation algorithm is
also given under this setting.
