Risk aversion of insider and dynamic asymmetric information

TL;DR

This paper develops a comprehensive equilibrium model for a risk-averse insider with a dynamic stochastic signal, extending previous models by removing risk aversion restrictions and providing explicit solutions.

Contribution

It introduces a novel approach using Schr"{o}dinger bridges to handle stochastic signals and risk aversion without restrictions, advancing the theoretical understanding of insider trading models.

Findings

Explicit equilibrium solutions for specific signal cases

Insider strategies are continuous with bounded variation

Market-maker pricing rules are characterized explicitly

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 Schr\"{o}dinger 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.