2. Consider a trader with initial fund given by To = 15, and the transaction cost function of holding q shares of stock i is C(q) = 10 + q². The price (x₂) at which this trader sells its position is stochastically distributed according to the following probability distribution: (0.5, 0.5, if x₂ = $2 if x₁ = $8 Let a random variable ♬ be the profit of trading at each time t, t = 1, 2, …, T, (a) If the trader's utility function is given by 1 u(ñ) = µ(ñ) — -—-0(ñ), P(x₁) = where μ() is the mean and o() is the variance, determine the trader's optimal level of position, and the associated equilibrium profits from liquidate the complete position.
2. Consider a trader with initial fund given by To = 15, and the transaction cost function of holding q shares of stock i is C(q) = 10 + q². The price (x₂) at which this trader sells its position is stochastically distributed according to the following probability distribution: (0.5, 0.5, if x₂ = $2 if x₁ = $8 Let a random variable ♬ be the profit of trading at each time t, t = 1, 2, …, T, (a) If the trader's utility function is given by 1 u(ñ) = µ(ñ) — -—-0(ñ), P(x₁) = where μ() is the mean and o() is the variance, determine the trader's optimal level of position, and the associated equilibrium profits from liquidate the complete position.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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if u can answer the first question it would be helpful. Thank you.
Transcribed Image Text:2. Consider a trader with initial fund given by To = 15, and the transaction cost function of
holding q shares of stock i is C(q) = 10 + q². The price (x;) at which this trader sells its
position is stochastically distributed according to the following probability distribution:
J0.5, if a; = $8
P(x;) =
0.5, if x; = $2
Let a random variable îñ be the profit of trading at each time t, t = 1, 2, ...,T,
....1
(a)
If the trader's utility function is given by
u(t) = M(#) - 당(%).
where u(:) is the mean and o(-) is the variance, determine the trader's optimal
level of position, and the associated equilibrium profits from liquidate the complete
position.
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