The cost of delay as risk measure in target-based multi-period portfolio selection models

Increasingly in recent years the fund management industry has evolved towards so-called goal-based investing paradigms, under which investors are assumed to base their portfolio strategies on pre-specified targets to be attained in the future. A similar decision model is common in the wealth management and the life insurance industries where targets may be associated with long term investment horizons and retirement planning problems. Based on this evidence, we propose in this article a novel risk measure explicitly focusing on the financial cost that may be associated with a delay in reaching those targets. We show that the definition of this risk measure is both rather natural and effective to capture investors’ risk preferences. A dynamic portfolio selection model is developed to assess the effectiveness of the risk measure from financial and risk control perspectives. The introduced risk measure has good properties and it is related to the Value-at-Risk (VaR) with a given confidence level. Under sufficiently general statistical assumptions, we derive a closed form solution to a mean-risk formulation of the portfolio problem in which the cost of delay is taken as risk measure. Finally, a set of numerical tests validate the proposed portfolio selection model and show a set of comparative results with respect to a classical dynamic mean-variance model.