Abstract
Except for several pairs of utility functions and distribution functions, expected utility maximization problems do not have closed-form solutions so that these problems often require complex numerical optimizations. The paper proposes an approximated solution to this problem using higher moments of returns. Utility functions are approximated by polynomials by the Taylor expansion, and thus, expected utility functions are approximated by linear combinations of moments. With the GARCH effects, a simple approach to estimate conditional higher moments is given. In an empirical study, the strategy is compared to alternative strategies such as mean variance optimization and static optimization.
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