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October 24th, 2010, 06:48 PM   #1
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Merton consumption model

Does anyone know why in Merton's optimal consumption and investment problem the consumption at time t can be bigger than the wealth at time t? How is it possible? For example, the proportion of wealth invested in the risky asset can be bigger than 1 because short selling is allowed. But what about consumption?
The model can be found in http://en.wikipedia.org/wiki/Merton's_portfolio_problem
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October 29th, 2010, 12:04 AM   #2
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Re: Merton consumption model

Do you have a source that says it can be. This seems to contradict the following statement on Wikipedia:

Quote:
He starts with a known initial wealth W0 (which may include the present value of wage income). At time t he must choose what amount of his wealth to consume: ct and what fraction of wealth to invest in a stock portfolio: ?t (the remaining fraction 1 ? ?t being invested in the risk-free asset).
It sounds like an interesting problem though. It is interesting the optimal solution is so simple.
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October 29th, 2010, 05:29 PM   #3
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Re: Merton consumption model

That's the point. It says "fraction of wealth" and "consume", thus, he may consume more than his wealth.
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November 19th, 2010, 11:54 AM   #4
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Re: Merton consumption model

Quote:
Originally Posted by Alex1
That's the point. It says "fraction of wealth" and "consume", thus, he may consume more than his wealth.
I think you are misreading it. It probably means fraction of their wealth although I suppose a person could consume more then their wealth if they went into debt.
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