A prediction market is a market where people can trade based on the outcomes of future events. It is widely used in sports games, elections, and the pricing of digital options. In math finance, prediction markets can be modeled by the so-called win martingales, continuous time martingales that end up with Bernoulli distributions. In this talk, choosing specific divergences as objective functionals, we will solve a class of optimal win martingale. In some cases, we will get explicit formulas of optimizers, and make connections between Schrödinger and filtering problems. Based on the joint work with Julio Backhoff.