# 4Q

Assignment Requirements

Q5. While performing initial feasibility analysis, it was assessed that two designs, A and B, have normal payoff distributions with {mean, standard deviation} of {4 million, 1 million} and {5 million, 2 million} respectively. Which design should be selected using risk-neutral valuation? Which design should be selected if the standard deviation for design B is 4 million? What does this tell you about risk-neutral valuation versus utility functions?

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Q6. Monika provides the following ordering of outcomes: X1, …….., X5 . Is she consistent with the five rules?

1. X1 ≻ X2 ≡ X3 ≻ X4 ≡ X5
2. X1 ≻ X2 ≡ X3 ≻ X4 ≡ X5
3. X1 ≻ X2 ≡ X3 ≻ X4 ≡ X5
4. X1 ≻ X2 , X2 ≻ X4, X4 ≻ X3, and .   X3 ≻ X4
5. .   X1 ≻ X2, .   X3 ≻ X4, and .   X3 ≻ X4

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Q7. For case a in problem 6, Monika provides the following preference probabilities for the intermediate options. Is she consistent with the five rules?

1. Ppref (X2 ) = 0.7, Ppref (X3 ) = 0.7, and Ppref (X4 ) = 0

1. Ppref (X2 ) = 0.7, Ppref (X3 ) = 0.5, and Ppref (X4 ) = 0.5
2. Ppref (X2 ) = 0.2, Ppref (X3 ) = 0.2, and Ppref (X4 ) = 0

1. Ppref (X2 ) = 0.1, Ppref (X3 ) = 1, and Ppref (X4 ) = 0

e Ppref (X2 ) = 0.7, Ppref (X3 ) = 0.7, and Ppref (X4 ) = 0

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Q15. A nuclear plant needs to be set up in the outskirts of a big city. The plant needs to be close to the city. The plant needs to be close to the city if the I2R and other logistical losses are to be kept to a minimum, which amount to \$1 million per km distance per year. Finally, the plant has a meltdown probability in the next 30 years of 0.02, which, if it happens, can cause loss of life and property in dollar amount of 3 billion (adjusted for inflation) that linearly decreases with distance from the city and drops to zero at 20 km. If the utility function over money (over 30 years) is exponential with risk tolerance equal to 50 million, determine where the plant should be located if the inflation adjusted profit per year is \$20 million.

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