Abstract :
Traditional models, such as the mean-variance framework, miss two crucial, related factors: richness of uncertainty and more realistic preferences. This project aims to study portfolio optimization and related problems, in a dynamic setting for an agent concerned by the occurrence of exogenous rare events, and who can access a wide class of investment products. The project adopts three novel approaches: incorporating heterogeneous preferences and a variety of assets (options and other derivatives) in a portfolio optimization model, exploring non-standard preferences such as loss aversion in dynamic settings, and analyzing portfolio responses to rare and sudden shocks, such as market crashes or pandemics. Methodologies employed include recursive preference frameworks and stochastic differential utility models, which disentangle risk aversion from intertemporal elasticity of substitution. Theoretical insights will be translated into practical numerical applications to assess their relevance to real-world financial markets. This research bridges the gap between risk and decision theory and the complex dynamics of financial markets, contributing to a deeper understanding of optimal portfolio design under ambiguity.