Utility Maximization Under Endogenous Uncertainty

TL;DR

This paper proves the existence of expected utility maximization in models where decision-making influences uncertainty, using minimal assumptions and broad conditions to enhance applicability in practical scenarios.

Contribution

It introduces a new continuity condition for choice-dependent probabilities, allowing for general existence results without common restrictive assumptions.

Findings

Established a general existence theorem for utility maximization with endogenous uncertainty

Identified practical conditions like density continuity and stochastic dominance for verification

Expanded the theoretical framework to include broader models without traditional assumptions

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.