This paper develops an endogenous selection model under asymmetric information, in which risk types are endogenously determined by individuals. By assuming heterogeneity in asset sensitivity that inheres in a two-argument utility function, we find that in equilibrium, an asset sensitive type of individual may invest in self-protection and become a low-risk, whereas an insensitive type never chooses to expend effort. Unlike the standard model of Rothschild and Stiglitz (1976), the present study demonstrates that the sensitive type (low-risk) demands more insurance than the insensitive type (high-risk) under advantageous selection. We also find other types of equilibrium such as adverse selection, separating equilibrium for a single premium rate, partial pooling equilibrium, and pooling equilibrium. In contrast to all previous papers, the equilibrium results obtained in this study reflect the reality that individuals make trade-offs between an income and an insurable asset.