The method of martingale in Asian option pricing;

Φ-atomic Decompositions and Concave Φ-inequalities for Martingales;

The Chinese Stock Market Weak-form Efficiency Analysis——Martingale Method;

Relations of Stationary Processes, Martingales and Mardov Processes;

Fundamental Inequalities of Martingales on Weak L_p Spaces

Using martingales and random walks,the author got an approximate formula about probability of that the insurer′s surplus reaches an upper barrier before the ruin and its precise estimation.

This paper consider the renewal model under constant interest force,and obtain the exponential upper bounds of ruin probability by matingale method.

Applying the martingle theory,the Lundberg inequality and the formula for the ruin probability were concluded.

In the paper,we analyse martingle characteristics of conditional diffusion process and gain some results.

In this paper, some strong limit theorems on the functional of nonhomgenous Markov chains in random environment is discussed by means of martingle method.

convergence martingal by means of moment function and analytical method.

We get the optimal investment consumption process and terminal wealth by using the convex dual function (Legendre transform) of the utility function and the theory of martingal.

Piecewise deterministic Markov processes(PDMP) have important application in risk theory, especially the theory of martingal on the basis of PDMP has offered the method to stylize for studying risk theory.