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Optimization problem
Hi all, Say given utility function, 3 assets class with mean/variance/covariance. (We can assume one of them is riskless) Find the asset allocation such that expected utility is maximized. Is there any paper on it? There's the famous Merton formula, but that's for 2 asset. How to extend it? Also, what other approach is available?? If we need to directly evaluate the normal cdf, it seems impossible. Thanks!- boy
Optimization problem
Bjork's "Arbitrage Theory in Continuous Time" (1998), Chapter 14 is an introduction to stochastic optimal control.P.14.7 is about Mutual Fund Theorems and considers cases with n assets (with and without risk free one).It is based on Merton (1971) work - he did it in case of more than 2 assets too.
Optimization problem
QuoteOriginally posted by: OlyaBjork's "Arbitrage Theory in Continuous Time".She's a quant ?
Optimization problem
... getting back to the question...I would try to set the problem up in Excel, with the 3 asset weightings in some cells and the utility in another. Then use the Solver to find the maximum utility.
Optimization problem
It is maximum Expected utility. I wonder how would you use Solver to find it...It should be not so complicated to find analytic solution in this case. For 2 assets when one of them is risk-free and assuming power utility function (U(w)=w^p/p) the answer is: c=(mu-r)/(sigma^2*(1-p)), where c is a proportion of wealth you keep in stock (happens to be constant over time). Anyone knows how this will look like for the case of 3 assets?