There are two types of threshold constraint.
A trade threshold constraint means that if an asset is traded at all, then at least some number of units of the asset must be traded. For example, we might constrain trading in a particular asset to buying at least 20 shares or selling at least 10 shares if we trade it at all. (Note that if the constraint is that we must buy at least 20 shares, then that is a forced trade.
A portfolio threshold constraint means that if the asset is in the portfolio at all, then the position size must be at least some value. For example, we might constrain a certain asset to have at least 100 shares in the portfolio if it is a long position, and at least 50 shares if it is a short position.
The number of assets traded and number of assets held constraints are often shortcuts for threshold constraints rather than being desirable in their own right.
threshold argument performs these constraints in Portfolio Probe.
They can alternatively be specified in terms of monetary value with the