Is this financial market viable?

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SUMMARY

The discussion centers on the viability of a financial market consisting of two risky stocks, with initial values of $S^1_0=9.52$ and $S^2_0=4.76$ currency units. The market operates under a simple interest rate of 5% over the period [0,1]. The potential future values of the stocks are defined under three market states, leading to a portfolio analysis that reveals the conditions for arbitrage opportunities. The conclusion emphasizes that a viable market is one without arbitrage, and the discussion highlights the need for understanding these concepts to evaluate market viability.

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  • Understanding of financial market concepts, specifically "arbitrage opportunities."
  • Familiarity with stock valuation and investment portfolios.
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  • Ability to analyze financial scenarios using mathematical models.
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  • Research the concept of "arbitrage pricing theory" in finance.
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Finance students, investment analysts, and anyone interested in understanding market viability and arbitrage opportunities in financial markets.

WMDhamnekar
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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 :)