Is this financial market viable?

[WMDhamnekar]

Consider a financial market with two risky stocks and such that values at t=0 $S^1_0= 9.52 $ currency units and $S^2_0=4.76$ currency units. The simple interest is 5% during the period [0,1].We also assume that during the period time 1, $S^1_1, S^2_1$ can take three different values depending on the market states $\omega_1, \omega_2,\omega_3$. $S^1_1(\omega_1)=20$ currency units, $S^1_1(\omega_2)=15$ currency units, $S^1_1(\omega_3)=7.5 $ currency units. $S^2_1(\omega_1)=6$ currency units, $S^2_1(\omega_2)=6$ currency units, $S^2_1(\omega_3)=4$ currency units. Is this market viable?
Answer. Viable financial merket means the market without arbitrage opportunities. Let $q_1$ and $q_2$ be the amounts invested in stock 1 and stock 2 respectively. Since the initial value of portfolio is zero, we should have $-9.52q_1$ and $-4.76q_2$ in the bank account.So our portfolio value at time 1 for all possible states are

$V_1(\omega_1)=10.004q_1+1.002q_2$$V_1(\omega_2)=5.004q_1+1.002q_2$

$V_1(\omega_3)=-2.496q_1-0.998q_2$


Now how to find out arbitrage opportunities?

 

[HOI]

What is the definition of "arbitrage opportunity"? That is a finance term, not mathematics so you cannot expect people here to know that.

 

[Wilmer]

Now how to find out arbitrage opportunities?

Contact Warren Buffett :)