Given any two sets of independent non-negative random variables and a non-decreasing concave utility function, we identify sufficient conditions under which the expected utility of sum of these two sets of variables is (almost) equal. We use this result to design a polynomial-time approximation scheme (PTAS) for utility maximization in a variety of risk-averse settings where the risk is modeled by a concave utility function. In particular, we obtain a PTAS for the asset allocation problem for a risk-averse investor as well as the risk-averse portfolio allocation problem.
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