Uploaded June 2025 | Updated September 2026, 2 weeks ago
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.
🔔 Subscribe for more insights on the future of data modeling. Keep up-to-date on SIAM/BFS Webinars at wiki.siam.org/siag-fm/index.php/Current_events#Forthcoming_Talks
Watch *previous SIAM FME webinars* at youtube.com/playlist?list=PLf_ipOSbWC85WhSODpb_AHqtraqSkTVZR
Learn more about *SIAM Activity Group on Financial Mathematics and Engineering* at siam.org/get-involved/connect-with-a-community/activity-groups/financial-mathematics-and-engineering
#MathematicalFinance #StochasticProcesses #InformationTheory #ProbabilityTheory #Martingales #RelativeEntropy #PredictionMarkets #StochasticControl #MongeAmpere #QuadraticVariation #JulioBackhoff
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.
🔔 Subscribe for more insights on the future of data modeling. Keep up-to-date on SIAM/BFS Webinars at wiki.siam.org/siag-fm/index.php/Current_events#Forthcoming_Talks
Watch *previous SIAM FME webinars* at youtube.com/playlist?list=PLf_ipOSbWC85WhSODpb_AHqtraqSkTVZR
Learn more about *SIAM Activity Group on Financial Mathematics and Engineering* at siam.org/get-involved/connect-with-a-community/activity-groups/financial-mathematics-and-engineering
#MathematicalFinance #StochasticProcesses #InformationTheory #ProbabilityTheory #Martingales #RelativeEntropy #PredictionMarkets #StochasticControl #MongeAmpere #QuadraticVariation #JulioBackhoff
