Jackson, who joins the market at the beginning of investment with an initial wealth To, plans...
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Jackson, who joins the market at the beginning of investment with an initial wealth To, plans to invest his wealth within twoperiod. He can reallocate his portfolio at the beginning of each period. The capital market consists of one riskfree asset and three risky assets. At time period t, the given deterministic return of the riskfree asset and the random return of three risky assets are denoted by st= 1.05 and et = [e, e, ]', respectively. Assume that the only information known about e, is the first unconditional moments E[et] and 3 x 3 positive definite covariance Cov (et) = σε 11 σε 12 σε 13 0,21 0,22 1,23 ot,31 0,32 1,33  = 0.0342 0.0355 0.0351 0.0355 0.0900 0.05400. 0.0351 0.0540 0.0576 Let z be the wealth of the investor at the beginning of period t. At time period t, if i is the amount invested in the ith risky asset, then ,?? is the amount invested in the riskfree asset. Define the excess return of risky asset as P₁ = [P1, P2, P3 [(elst), (e?  st), (est)]' with its expected value E[P] = [0.14, 0.16, 0.17]. The twoperiod model of assets is to seek the best strategy, = [(?). (?)*, (i)*}', t = 0, 1, which is the solution of the following dynamic stochastic optimization problem, E[(22150)2²], min s.t. It+1=(²²²³)+₂₂ = 8₁₁ + Pit, Assume that the investor has initial wealth ro= 100. t=0, 1. (i) What is the optimal strategy of every period? [10 marks] (ii) What are values of E[x2] and Var(x2) according to the optimal strategy? [10 marks]
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