Utility maximization with a given pricing measure when the utility is not necessarily concave

作者：Reichlin Christian^*

来源：Mathematics and Financial Economics, 2013, 7(4): 531-556.

DOI：10.1007/s11579-013-0093-x

• Portfolio selection
• Non-concave utility
• Asymptotic elasticity
• Non-convex optimization
• Behavioural finance

We study the problem of maximizing expected utility from terminal wealth for a not necessarily concave utility function U and for a budget set given by one fixed pricing measure. We prove the existence and several fundamental properties of a maximizer. We analyze the (not necessarily concave) value indirect utility) u(x, U). In particular, we show that the concave envelope of u(x, U) is the value function u(x, U-c) of the utility maximization problem for the concave envelope U-c of the utility function U. The two value functions are shown to coincide if the underlying probability space is atomless. This allows us to characterize the maximizers for several model classes explicitly.

• 出版日期2013-9