Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy regularization for Mean Field Game (MFG) with learning in a...

We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency...

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a novel framework, in which a robo-advisor interacts with a...

In an Ito-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversi?cation settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria,...