Disagreement in Asset Prices with Endogenous Beliefs

PART I - This first part develops a micro-founded asset-pricing framework for incomplete markets in which subjective beliefs are chosen optimally. Agents select probability measures to maximize an entropy-weighted objective, so preferences discipline how probability mass is allocated across states and how uncertainty is encoded.
Heterogeneity in these optimal belief tilts generates disagreement even under a shared no-arbitrage benchmark and enters prices through an information-based stochastic discount factor (InSDF). In equilibrium, disagreement is priced as an informational premium: assets that perform poorly in states where belief wedges are large must offer higher expected returns.
A central aim of this thesis is to address the unresolved problem of measuring disagreement by combining objective objects, such as probability distributions, with subjective elements, such as preferences, thereby yielding a quantifiable metric for characterizing disagreement.
Relative to the complete-markets benchmark with a common prior, the model explains persistent belief heterogeneity without relying on exogenous private signals. Risk-averse agents choose less concentrated (higher-entropy) beliefs, while more risk-tolerant agents tilt probability mass toward favorable outcomes. A central object is the disagreement wedge κ, a closed-form, state-dependent likelihood ratio between agents’ optimal beliefs that maps directly into the pricing kernel.

Finally, the paper characterizes conditions under which belief disagreement converges. In the absence of new information, entropy-based discipline shrinks belief wedges and recovers the benchmark pricing kernel. Overall, the framework links preferences, subjective probabilities, and asset prices in a tractable no-arbitrage setting and interprets disagreement as a priced informational friction.

PART II - This paper develops the applied implications of a belief-based asset pricing framework in which agents optimize entropy-weighted utility functions under subjective uncertainty. Building on prior theoretical work, it incorporates informational disagreement into four related settings: the Cox–Ross–Rubinstein (CRR) option pricing model, the Capital Asset Pricing Model (CAPM), expected utility under ambiguity, and the dynamic convergence of beliefs.
First, we introduce a disagreement-tilted binomial pricing model in which agents hold distorted beliefs derived from entropy-penalized utility. A belief-distortion parameter κ modifies the benchmark pricing measure, generating heterogeneous valuations and providing a structural explanation for trading volume and persistent dispersion in expectations. Second, we derive an information-adjusted CAPM (InCAPM) in which the pricing kernel embeds both risk preferences and informational asymmetries. The resulting informational beta captures belief dispersion as a priced factor, leading to a generalized risk premium. Third, we present a minimal resolution of the Ellsberg paradox using an entropy-based adjustment to utility, which generates ambiguity aversion without violating additivity or Bayesian updating. Fourth, we develop a theory of belief convergence showing that, in the absence of new information, disagreement cannot persist indefinitely under common pricing discipline. As informational wedges compress over time, subjective
valuations align and market prices converge toward their benchmark no-arbitrage relation, providing a microfoundation for informational efficiency as an endogenous limiting outcome.
Taken together, these results offer a unified framework in which belief heterogeneity, entropy, ambiguity, and convergence are treated as core components of asset pricing rather than as anomalies. Classical models emerge as limiting cases when disagreement vanishes or beliefs converge.