Dynamic asset risk-seeking insider trading under signal observation

In this paper, we investigated a continuous version of an insider trading model. There were three basic assumptions in this model: (1) the insider exhibited risk-seeking, (2) market makers could receive partial signals regarding the risky asset, and (3) the risky asset was driven by a standard Brownian motion. By employing optimal filtering theory and stochastic control theory, we derived some necessary conditions for market equilibrium. Additionally, we established both the existence and uniqueness of the market equilibrium. At equilibrium, we observed that as time progresses, the insider's residual information gradually diminished when the volatility of the risky asset was low. In contrast, if the volatility was high, the insider's residual information initially increased. Meanwhile, the partial observation coefficient remained constant, while both trading intensity and market liquidity increased over time.