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Time Cardinality Constrained Mean-Variance Dynamic Portfolio Selection

An investor does not always invest in risky assets in all time periods, often due to the management fee charged for hiring an agent in managing his investment in risky assets. Motivated by this observed common phenomenon, this paper considers the time cardinality constrained mean-variance dynamic portfolio selection problem (TCCMV) in which the number of time periods where investment in risky assets is allowed is limited. Both the analytical optimal portfolio policy and the analytical expression of the efficient mean-variance frontier are derived for TCCMV problem. By implementing such a solution procedure for different cardinalities, the mean-variance dynamic portfolio selection problem with management fees can be efficiently solved.