# Value At Risk Rigorous Definition

Reading a paper about VaR and don't understand what $$a'$$ is. The link to the paper is here: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.878.8823&rep=rep1&type=pdf. The relevant passage is:

We consider n financial assets whose prices at time $$t$$ are denoted by $$p_{i,t}$$ ,is $$1, . . . ,n$$. The value at $$t$$ of a portfolio with allocations $$a$$ , i =$$1, . . . ,n$$ is then:
$$W_f(a)=\sum_{i=1}^n{a_ip_{i,t}}=a'p_t$$ If the portfolio structure is held fixed between the current date $$t$$ and the future date $$t+1$$, the change in the market value is given by $$W_{t+1}(a)-W_t(a)=a'(p_t+1-p_t)$$

Apologies for basic question, I just don't understand what $$a'$$ is supposed to be and why you can separate the $$p_{i,t}$$ term.

• $a$ is a vector of portfolio weights (allocations) and $a'$ is $a^\top$, the transpose of the vector. Then, $\sum\limits_{i=1}^n a_ib_i=a'b$ is just the Euclidean inner product. Jun 30 at 21:30
• @Kevin Oh gotcha, thank you. Jun 30 at 21:50
• Also, that $p_t +1$ should be $p_{t+1}$.
– ir7
Jun 30 at 22:16