Securities Prices in Financial Markets
The total wealth (as is pointed out in the book) is given as :

$$
X(1)=\delta_{0}B(1)+\delta_{1}S_{1}(1)+...\delta_{N}S_{N}(1)
$$
The wealth at period one is just the sum of the securities (including amount invested in the bank) times their number. In other words, the total wealth is the amount of money this individual has invested in the different assets. It has nothing to do with a "changing process." Asssume that the individual does not buy any more assets during period 1 and the assets promise a return of $(1+r_{i})$ where $i$ denotes the asset in question. In period 2, the individuals wealth is then
$$
X(2)=\delta_{0}B(1)(1+r_{0})+\delta_{1}S_{1}(1)(1+r_{1})+...\delta_{N}S_{N}(1)(1+r_{N})
$$