We propose a formal theory of asset pricing that allows us to explain how sentiments in the market may influence price formation. A fully nonlinear expectation captures behavioral market sentiments in terms of waves between optimism and pessimism. The approach follows the standard procedure by extracting some stochastic Euler equation from a representative agent equilibrium model. Preferences are represented through sentiment-based expected utility. In equilibrium, the resulting asset price process can then be described by a new (nonlinear) conditional sentiment-based expectation. In a final step, we observe the possible emergence of a bubble that is induced by disagreement of optimism and pessimism for the market relevant pricing measures.
Joint work with Patrick Cheridito.