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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 numberof different values. We show that if each asset can take only two values, theproblem becomes polynomial-time solvable. However, even if each asset can takethree different values, DSHP is still NP-hard. An approximation algorithm isalso given under this setting.

The Discrete Sell or Hold Problem with Constraints on Asset Values