The Nature Of The B-valued Martingale Sequence, And The Martingale Approach In The Financial Markets

In 1966, Rieffef difined a geometric concept called dentability in banach space. Then he proved the equipollence of dentability and RNP with the tool is martingale. Since then the interdependent and opposite relations between probability characters of martingale sequence and geometric properties of banach space becomed the focus which people were paying close attention to, and they have achieved fruitful results so far. In recent years, martingale approach has been widely applied to financial markets,that shows the great role of martingale theory. In this paper, While we try to further explore the nature of B-valued martingale, on the other hand to discuss the financial markets martingale method for finding the optimal investment program on the application.In the first chapters, we briefly describes the nature of a series of B-valued martingale and some important achievements has been made by scholars in the past.In the second chapter, by studying the relationship between B-valued martingale sequences, inspired by Professor GAN shi-xin's monographs,I restrict B to be finite-dimensional's Banach space, get two characters from the B-valued martingale sequences, one is reflected in the B-Value'sa Kp sequence, and another B-valued quasimartingale, and giving proof for them. In the third chapter, We restrict B to be finite-dimensional's Banach space, by studying the relationship between B-valued martingale sequences and the convergence, Radon-Nikodym property and smoothness of the B-valued martingale, we get a concise necessary and sufficient condition and an inequality of B-valued martingale.In the fourth chapter, there is an investor who has an initial wealth of X0<1, and he wants to obtain the maximal probility of achieving a goal, that is XT=1.When the stock's dift is not observed directly but only vi the measurement process. Adopting a martingale approach, and a Generalized Gameron-Matin Formula then enables explicit computation of the value of the problem as well as the wealth process. The dynamic optimal allocation can then be determined using Clark's formula.