Based on a classical financial market model different model variants known from the literature are discussed and analyzed, each focussing on modeling financial markets as a nonlinear dynamic system by introducing the formation of (heterogeneous) beliefs about future asset prices into the model framework. Furthermore, a market model under a market maker scenario is proposed which brings these types of financial market models to a more consistent and more realistic model structure. The proposed market model explicitly takes into account the risky-asset supply side. This extension in the model structure allows to model the risk premium demanded by the market participants for taking market risk, which appears to be endogenously driven by the market over time. The resulting dynamics of asset price and agents' wealth is analyzed within a chartist-fundamentalist framework. Within this model framework it becomes possible to characterize the market equilibria and the other kinds of asymptotic behavior in terms of the long-run evolution of wealth proportions and risky-asset returns. Moreover it is shown to which extent those heterogeneous expectations in the agent-based market model can explain observed fluctuations in real financial markets and lead to the emergence of complicated dynamics of growing asset price paths.