Martingale Pricing Theory

Abstract

From ages to ages there had been expectation of individuals on a specific predictions and future occurrences. So also in a game, different participant that involves in those specified game have their various expectations of the results or the output of the game they are involved in. That is why we need a mathematical theory that helps in prediction of the future expectations in our day to day activities. Therefore the Martingale Theory is a very good theory that explains and dissects the expectation of a gamer in a given game of chance. So in this thesis, we shall talk about the Martin-gale Theory expressing the expectations of a gamer in a game of chance, and also discuss the gaming strategies so as to enlighten everyone involved in a specific game their required expectation after proper understanding of the Martingale Theory. Also this thesis examines testing Martingale Difference Hypothesis (MDH) and related statistical inference issues and it discusses the developments of tests and applies them to exchange rate data.