Case: John Harrison is a portfolio manager of an IT development company and currently holds a portfolio consisting of $n$ risky assets $($represented by $i=1,$dots,$n)$ and cash investment $($denoted by $i=0).$ He would like to determine holdings $($defined as the contents of an investment portfolio held by the investor$)$ over a financial planning horizon of $T$ years. The portfolio can be restructured at discrete time periods $t=1,$dots,$T$ in terms of holdings; in particular, $t=0$ represents today. Let $p_{it}$ denote price of a share of asset $i$ at time $t.$ It is assumed that cash account