This presentation in plain language stresses on intuition rather than abstraction or calculation. It is conducted mainly in Mandarin. The PPT is English based. Martingales are a class of stochastic processes related to financial engineering, Brownian motions and random walks. The plain interpretation of a martingale is “fair gamble.” The fundamental martingale stopping theorem says that when you are engaged in fair gamble, the expected net winning will be zero regardless when and how you choose to stop the games.

 

Many problems pertaining to probability can be modeled by Markov chains. This widely applicable approach though is sometimes too loose in grasping the essence of the problem and thereby incurs unnecessary lengthy calculation that erodes the intuition. When the problem can be modeled by a martingale, the solution pops out instantly. Classic examples to be presented include martingale of patterns, graduation cap tossing, gambler’s ruin, and the ballot problem. A biproduct scientifically upholds the tortoise in the race against the hare.

 

The talk is accessible to general audiences. 

 

Organizer: Chun-Yen Shen (NTU)