Optimization of win martingales

Prediction market is a market where people can trade based on outcomes of future events. It is widely used in sports games, elections, and pricing of digital options. In math finance, prediction markets can be modeled by the so-called win martingales, which are continuous time martingales that end up with Bernoulli distributions. In this talk, choosing different divergences as objective functionals, we will solve a class of optimal win martingales. In some cases, we will get explicit formulas of optimizers, and make connections to Schrödinger, filtering problems, Wright-Fisher diffusion, and the problem of identifying most exciting games.