Heterogeneous beliefs in financial equilibrium models describe the situation where agents hold different views about the probability distribution governing asset dynamics. In the transaction cost models of Shelley (2023) and Muhle-Karbe, Nutz, Tan (2020), beliefs are modelled as locally equivalent probability measures obtained via Girsanov’s theorem.
Each agent n views the risky asset under a probability measure P^n ~ P (locally equivalent), so that the asset price has drift mu_t^n = mu_t + sigma * epsilon_t^n under P^n, where epsilon^n is agent n’s belief process. The agents “agree to disagree” in the sense of Aumann — they do not update their beliefs from observing prices or each other’s trades.
Heterogeneous beliefs play a dual role:
- Speculative trading motive: agents with optimistic beliefs hold larger positions, creating trading volume beyond what hedging alone would generate. This is “non-fundamental trading” in the sense of Davila.
- Liquidity premium generation: under transaction costs, belief heterogeneity generates nontrivial liquidity premia even when risk aversions are identical (Corollary 5.4 in Herdegen et al.).
The normative question of whether a transaction tax is beneficial depends on the interaction between belief heterogeneity and hedging needs. The tax is beneficial precisely when it penalises false beliefs more than it impedes hedging.
Key Details
- Modelling: Girsanov measure changes epsilon^n shift the drift by sigma * epsilon
- Admissible beliefs: epsilon in the set B of predictable, locally bounded L^4 processes with E(epsilon . W) in M_delta
- Key result: with homogeneous beliefs (epsilon^n = 0 for all n), equilibrium prices do not depend on transaction costs
- Heterogeneous beliefs + costs: generate non-trivial liquidity premia and potential welfare benefits of taxation
- Dual role of costs: transaction costs increase volatility (forward-looking agents anticipate future trades), holding costs decrease it (discounting future opportunities)