Market Equilibrium

Mean-Field Price Formation on Trees with a Network of Relative Performance Concerns ArXiv ID: 2512.21621 “View on arXiv” Authors: Masaaki Fujii Abstract Financial firms and institutional investors are routinely evaluated based on their performance relative to their peers. These relative performance concerns significantly influence risk-taking behavior and market dynamics. While the literature studying Nash equilibrium under such relative performance competitions is extensive, its effect on asset price formation remains largely unexplored. This paper investigates mean-field equilibrium price formation of a single risky stock in a discrete-time market where agents exhibit exponential utility and relative performance concerns. Unlike existing literature that typically treats asset prices as exogenous, we impose a market-clearing condition to determine the price dynamics endogenously within a relative performance equilibrium. Using a binomial tree framework, we establish the existence and uniqueness of the market-clearing mean-field equilibrium in both single- and multi-population settings. Finally, we provide illustrative numerical examples demonstrating the equilibrium price distributions and agents’ optimal position sizes. ...

Risk aversion of insider and dynamic asymmetric information ArXiv ID: 2512.05011 “View on arXiv” Authors: Albina Danilova, Valentin Lizhdvoy Abstract This paper studies a Kyle-Back model with a risk-averse insider possessing exponential utility and a dynamic stochastic signal about the asset’s terminal fundamental value. While the existing literature considers either risk-neutral insiders with dynamic signals or risk-averse insiders with static signals, we establish equilibrium when both features are present. Our approach imposes no restrictions on the magnitude of the risk aversion parameter, extending beyond previous work that requires sufficiently small risk aversion. We employ a weak conditioning methodology to construct a Schrödinger bridge between the insider’s signal and the asset price process, an approach that naturally accommodates stochastic signal evolution and removes risk aversion constraints. We derive necessary conditions for equilibrium, showing that the optimal insider strategy must be continuous with bounded variation. Under these conditions, we characterize the market-maker pricing rule and insider strategy that achieve equilibrium. We obtain explicit closed-form solutions for important cases including deterministic and quadratic signal volatilities, demonstrating the tractability of our framework. ...

Equilibrium with non-convex preferences: some insights ArXiv ID: 2503.16890 “View on arXiv” Authors: Unknown Abstract We study the existence of equilibrium when agents’ preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single-valued nor convex-valued. Keywords: General Equilibrium, Non-Convex Preferences, Demand Correspondence, Market Equilibrium, Utility Functions, General Equilibrium Theory ...