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Optimal Portfolio for an Investor

Explain how a given investor chooses an optimal portfolio. Will this choice always be a diversified portfolio, or could it be a single asset?

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Explain how a given investor chooses an optimal portfolio. Will this choice
always be a diversified portfolio, or could it be a single asset?
The Robinson Crusoe Economy V's Capital Markets
How does a single individual choose an optimal portfolio or risky assets in a world where there are no opportunities for exchange involving risk sharing? Note the nature of the constraint here - we require individuals to exactly satisfy their wealth/budget constraints at each date in the following sense.
1. A Portfolio : Given a particular stick of wealth at any date, W, a portfolio constitutes an allocation of wealth among a number of assets, i=1,...N, such that proportion of wealth allocation to each asset (i) is
(i) i 0 : non-negative
and
(ii)
(i)above ...

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