The following represents a model for an economy.
At time $t=0$, four assets have the value $X_1= £5$, $X_2=£5$, $X_3=£10$ and $X_4=£4$.
Three possible states of the world exist ($\alpha_1$, $\alpha_2$ and $\alpha_3$) at time $t=1$, with this being viewed at $t=0$, and these states can occur with probabilities $p_1=0.25$, $p_2=0.5$ and $p_3=0.25$ (respectively).
In state $\alpha_1$, the values of asset at $t=1$ are $X_1=£6$, $X_2=£3$, $X_3=£12$ and $X_4=£9$.
In state $\alpha_2$, the values of asset at $t=1$ are $X_1=£9$, $X_2=£6$, $X_3=£12$ and $X_4=£3$.
In state $\alpha_3$, the values of asset at $t=1$ are $X_1=£12$, $X_2=£6$, $X_3=£9$ and $X_4=£3$.
Assume it is possible to own a part of an asset but it is not possible sell an asset which you do not own.
Show that it is possible to set up a portfolio of assets at $t=0$ which will definitely have a value of $£30$ at $t=1$, no matter which state of the world occurs at time $t=1$.
What is the guaranteed profit/loss of this portfolio?
I'll be honest, I'm at a total lose with this topic. A point in the right direction would be great. Maybe published text or a similar solution on this website? (If one exists?). Thank you.