MHB Is this financial market viable?

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The discussion centers on the viability of a financial market with two risky stocks, given their initial values and potential future states. The market's viability is assessed based on the absence of arbitrage opportunities, which occurs when a portfolio can be constructed that guarantees a profit without risk. Calculations for the portfolio value at time 1 across different market states indicate potential negative outcomes, suggesting the presence of arbitrage. The conversation highlights the need for a clear understanding of arbitrage opportunities in finance, which may not be familiar to all participants. Overall, the market's viability remains uncertain due to the potential for arbitrage.
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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?
 
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What is the definition of "arbitrage opportunity"? That is a finance term, not mathematics so you cannot expect people here to know that.
 
Dhamnekar Winod said:
Now how to find out arbitrage opportunities?
Contact Warren Buffett :)
 

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