# Securities Prices in Financial Markets

Hello in the moment I am working with the book "Introduction to the Economics and Mathematics of Financial Markets" by Jakˇsa Cvitani ́c and Fernando Zapatero, which can be accessed at the link.

However, at the moment I am struggling with the third chapter "Models and Securities Prices in Financial Markets". Right in the beginning at page 56 there is an introduction of a formula, which I do not understand completely.

X(1) should display the worth of all the assets (securities,stocks, bonds etc.). Therefore B=Bonds, S=Securities or Stocks. The numbers 0 and 1 illustrate the time. So 1 for the end and 0 for the beginning.

But what is the this sign "δ". Actually it is a delta isn't it? And it actually illustrates a changing process. However, here it is described as follows "Denote by δi , i = 1, . . . , N the number of security i shares that Taf holds between time zero and time one. We denote by δ0 the amount invested in the bank account at time zero, “the number of shares” of the bank account." (page 55, at the same book). My problem is that I really do not understand the meaning of this sign. Also the Sentence, which is illustrated in the picture talks about a vector. I completely do not understand the word vector in this relationship.

I hope I can get some insight to this topic through your help. Overall it should be an introduction to the two periods binomial models.

$$X(1)=\delta_{0}B(1)+\delta_{1}S_{1}(1)+...\delta_{N}S_{N}(1)$$ 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 $$X(2)=\delta_{0}B(1)(1+r_{0})+\delta_{1}S_{1}(1)(1+r_{1})+...\delta_{N}S_{N}(1)(1+r_{N})$$