Multiperiod mean-standard-deviation time consistent portfolio selection

We study a multiperiod portfolio selection problem in which a single period mean-standard-deviation criterion is used to construct a separable multiperiod selection criterion. Using this criterion, we obtain a closed form optimal strategy which depends on selection schemes of investor's risk preference. As a consequence, we develop a multiperiod portfolio selection scheme. In doing so, we adapt a pseudo dynamic programming principle from other existing results. The analysis is performed in the market of risky assets only, however, we allow both market transitions and intermediate cash injections and offtakes.