In this paper,by taking the stationary field for example,equal calculation of polari- sation medium additional field is studied,then dual methods between electric field and magnetic field are described.

In this paper,a dual method for sloving a class of convex quadratic programming problems is given.

By discussing the content of dual operations,dual figures and dual principle,the article puts forward the concept of dual method, and expound further the use of dual principle and dual method in the higher geometry and wide use in other subject

By supposing that the risk the contract may be terminated is not the risk of the system and using martingale methods and the pricing formula of the European contingent claim with stochastic lives,the pricing problem of two kinds of exotic options with stochastic lives is discussed,in which the underlying asset follows the Merton models.

In the case when the interest rate is stochastic,which satisfies It stochastic differential equation,and suppose the stochastic factor affecting interest rate is related to the factor affecting stock price,the pricing formula of Call Option With Proportional Payoff under stochastic interest rates is deduced by applying the martingale method.

By minimizing the absolute replication error,the optimal hedging volatility is yielded,namely the adjusted volatility,and then this adjusted volatility with martingale approach is integrated to achieve the optimal portfolio in presence of transaction costs and trading rest.

By martingale approach,Lundbery s fundamental equation is gotten and two effective applications of its solutions are presented.

By martingale approach,Lundberg s fundamental equation is got and two effective applications of its solutions are considered.

The Lundberg inequality and formula on the ruin probability are obtained by using the method of martingale.

Under the circumstances of time-dependent interest rate r(t) of riskless asset,dividend payment of risk asset,time-dependent expected return μ(t),volatility σ(t) and dividend yieldρ(t),the authors use martingale to establish a pricing model of geometric Asian options with floating strike price.

The martingale methods and the joint distribution of the maximum with the terminal value of its underlying Brownian motion with drift were applied to varied barrier option driven by Ornstein-Unlenback process,thus a simple and effective piecing expressions was derived.

In this paper,we suppose the risk of the contract that may be terminated is not the risk of the system,by means of martingale methods and the pricing formula of European contingent claim with stochastic lives,the pricing problem of Payoff Segment Calls with stochastic lives is discussed which the underlying asset follows the Merton models and the corresponding pricing formulas are obtained.