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.

In this paper,the formulas of the pricing European option are obtained by insurance actuary pricing without any other market assumption.

An actuarial approach to compound option pricing;

In this paper,assume that the interest is given,using physical probability measure of price process and the principle of fair premium——an actuarial approach,we deal with pricing formula of European option on foreign currency,and obtain pricing of European call and put option.

Improvement to a ruin model in insurance actuarial;

Some commonly used order relations of risks in actuarial theory are discussed.

By the theory of stochastic optimal control and actuarial theory,the paper studies the investment strategy for the life insurance premium,based on the semi-continuous term life insurance mode and power law utility function.

Based on the insurance actuarial theory and the classic financial engineering theory,the paper analyses the value of life insurance policies with embedded surrender option,and finds out that whether the surrender option is exercised is related to several factors in a certain policy,in which the relation varies with the change of factors value.

This paper first gives an explanation of moral hazard in the insurance field,and then offers a game theory model about insurance pricing according to the non zero sum game analysis between the insurer and the insured when moral hazard exists.

With the integration of contemporary insurance economics with financial economics,introducing the concept of finance-type insurance products and applying finance theory to insurance pricing can make up for the shortcoming of the traditional insurance pricing model which was ignorant of investment return.