The paper used the Girsanov theory of stochastic analysis and the martingale pricing method,which was put forward by Harrison and Kreps in 1979,to induce the pricing equations for generalized reset bull call options and generalized reset bear put options.

Obtain the martingale pricing formulas and the insurance actuary pricing formulas to two kinds of mortgage insurance,and also prove that they go all the way when the unpaid money is a constant and the house price is driven by a genegal It process.

We study single-point-level reset options pricing problems by using the martingale pricing method and the probability distribution of extremes.

By applying the martingale pricing method in a world in which the logarithmic normal diffuse processes are expressed risk-neutral,we get European exchange rate call option related with the stock.

With quasi-martingale method,this paper solves an option pricing model in the fractional market,which makes original Black-Scholes equation as an special example.

In this paper, some inequalities are established between a p-quasi-martingale and its p-power function.

Let 1quasi-martingale f=fnn≥0∈pHσαX, f can be decomposed into fn=sum form k∈Z to μkank(n≥0) and ‖f‖pHασ(X)+‖Rf‖α～inf(sum form k∈Z to μkα)1/α, where ak=(ank)n≥0(k∈Z) is a sequence of 1, α, ∞; p quasi-martingale atoms with supk∈Z‖ak*‖α<∞ and μkk∈Z∈lα are nonnegative numbers.