The Discrete Sell or Hold Problem with Constraints on Asset Values

TL;DR

This paper investigates the discrete sell or hold problem with limited asset value options, revealing polynomial solvability for two-value assets and NP-hardness for three-value assets, along with an approximation algorithm.

Contribution

It establishes the complexity boundaries of DSHP with constrained asset values and provides an approximation algorithm for the three-value case.

Findings

Two-value asset case is polynomial-time solvable.

Three-value asset case remains NP-hard.

An approximation algorithm is proposed for the three-value case.

Abstract

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.