Polynomial Utility

We approximate the portfolio utility maximization problem by series expansions of the utility function of which the second order Taylor expansion is a special case leading to mean-variance utility. Conforming with the modern approach to dynamic mean-variance optimization we approach the problem by equilibrium theory. We study the convergence of two expansions via Taylor and Bernstein polynomials, respectively, discuss their weaknesses, and propose ways to circumvent them. We illustrate the insight obtained in numerical studies covering both power utility and S-shaped utility with an adapted reference point.