The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals under uncertainty; this is the case even if the asset market is incomplete.
Chiappori, P.-A., Ekeland, I., Kubler, F., & Polemarchakis, H. M. (2000). The identification of preferences from equilibrium prices under uncertainty (CORE Discussion Papers 2000/25). https://hdl.handle.net/2078.5/128209