Utility Maximization Under Endogenous Uncertainty

Abstract: This paper establishes a general existence result for expected utility maximization in settings where the agent's decision affects the uncertainty faced by her. We introduce a continuity condition for choice-dependent probability measures which ensures the upper semi-continuity of expected utility. Our topological proof imposes minimal restrictions on the utility function and the random variable. In particular, we do not need common assumptions like the monotone likelihood ratio property (MLRP) or the convexity of distribution functions condition (CDFC). Additionally, we identify sufficient conditions - continuity of densities and stochastic dominance - which help verify our assumptions in most practical applications. These findings expand the applicability of expected utility theory in settings with endogenous uncertainty.