Скачать или смотреть Entropy, Martingales, and the Most Exciting Game with Julio Backhoff

In this talk, Julio Backhoff explores specific relative entropy—a refined notion of entropy arising from the discretization of continuous-time martingales. While laws of continuous martingales are typically mutually singular (yielding infinite relative entropy), the discrete-time setting opens the door to meaningful comparisons via a scaled entropy limit.

Backhoff discusses:
A closed-form expression for specific relative entropy in terms of the martingales’ quadratic variation.
Its intriguing application to prediction markets, answering David Aldous's question on identifying the "most exciting" game—i.e., the market with the highest entropy—through a stochastic control framework.
A further extension to multi-outcome games, revealing a novel connection to Monge-Ampère equations via joint work with Wang and Zhang.

This talk blends probability, information theory, and mathematical finance, offering deep insights for researchers in stochastic processes and market modeling.

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