Abstract: Within the framework of the bounded rationality, the survival ability and market impact of investors are studied with the learning process of the Kalman-Bucy filter, the rational level and confident level of an investor are defined and an explanation to the coexistence phenomenon of different investors in the financial market is given. The results show that the survival ability of an investor depends on his rational and confident levels both. The more rational and more confident an investor is, the higher his survival probability is, and furthermore, the larger his market impact is. If an investor with a high rational level is not confident but the other investor with low rationality is very confident, then nobody has a comparatively accurate estimation about the future return of the risky asset. In this case, it is too hard to say who can survive in the market and in fact, different investors will coexist and control the market in turn.

Key words: heterogeneous beliefs, Kalman-Bucy filter, rational level, confidence level, survival