Non-concave Expected Utility Optimization with Uncertain Time Horizon

Abstract We consider an expected utility maximization problem where the function is not necessarily concave and time horizon uncertain. establish a necessary sufficient condition for optimality general non-concave in complete financial market. show that concavification approach of to deal with non-concavity, while being still applicable when stopping respect market filtration, leads sub-optimality independent risk, hence can be directly applied. For latter case, we suggest recursive procedure which based on dynamic programming principle. illustrate our findings by carrying out multi-period numerical analysis optimal investment under convex option compensation scheme random horizon. observe distribution portfolio both certain uncertain right-skewed long right tail, indicating investor expects frequent small losses few large gains from investment. While (certain) average at premature date unimodal, multimodal distributed provides flexibility switching between local maximizers, depending performance. The structure multiple peaks different heights explained procedure, whereas has significant impact amplitude modes.