Incomplete information and heterogeneous beliefs in continuous time finance

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Continuous-time finance, developed by R. C. Merton in the late sixties and early seventies, has become a standard analytical tool in portfolio theory and asset pricing due to its elegance and convenience. Historically, this framework largely overlooked investors' beliefs, primarily because it evolved alongside option pricing, which assumed that expectations were irrelevant. Recently, the emergence of martingale pricing techniques, where expectations are crucial, has reintroduced the significance of beliefs in finance. Professor Alexandre Ziegler's habilitation thesis focuses on the role of expectations within continuous-time finance. After reviewing existing literature, the author examines how incomplete information and heterogeneous beliefs impact optimal portfolio and consumption choices, as well as equilibrium asset pricing. By relaxing the assumption of perfect observation of expected dividend growth, Ziegler illustrates that incomplete information influences stock prices and their dynamics, potentially explaining the late 1990s asset price bubble. Additionally, he explores how differing beliefs among investors shape their optimal portfolio selections and consumption behaviors.