Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R₁ with probability 1- q and Ro with probability q. We assume R₁ <0, Ro > 0. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset.

Microeconomic Theory
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ISBN:9781337517942
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Chapter7: Uncertainty
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Consider the following portfolio choice problem. The investor has initial wealth w and
utility u(x) = . There is a safe asset (such as a US government bond) that has net
real return of zero. There is also a risky asset with a random net return that has only
two possible returns, R₁ with probability 1- q and Ro with probability q. We assume
R₁ <0, Ro > 0. Let A be the amount invested in the risky asset, so that w - A is
invested in the safe asset.
1) Find A as a function of w
Transcribed Image Text:Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R₁ with probability 1- q and Ro with probability q. We assume R₁ <0, Ro > 0. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset. 1) Find A as a function of w
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