在假设股票价格服从带非齐次Poisson跳－扩散过程且在连续时间支付红利的情况下，建立了股票价格行为模型，同时应用保险精算法给出一类奇异期权———欧式幂期权———看涨和看跌两种情形的定价公式，以推广Merton关于期权定价的结果。得到的结果优于无红利支付的情况，使该定价公式更接近市场实际情况。

Assuming that the stock company pays dividend continuously and the dividend was related with the price of the stock in the time that the stock company pays dividend,and the pricing process was jump-diffu-sion process,the jump process was Poisson process,the stock pricing model was established.And it gave the European call power option and the European put power option pricing model using insurance actuary pri-cing.The result of Merton on European option pricing was generalized.It was superior to no-dividend payment and it was more closed to the actual market situation.

定义了Leibniz color代数和Leibniz Poisson color代数,并通过新定义的乘法运算得到了构造Leibniz color代数和Leibniz Poisson color代数的方法.

This paper presents the definition of Leibniz color algebra and Leibniz Poisson color algebra, and the method to construct the Leibniz color algebra and the Leibniz Poisson color algebra by the newly defined product.

广义复合Poisson风险模型被推广到两险种广义复合Poisson风险模型,并给出了理赔额分别服从指数和混合指数分布且初始资金为u的破产概率ψ(u)的明确表达式以及安全系数.

The generalized compound Poisson risk model was generalized to double -type insurance com-pound Poisson risk model .Explicit expressions of ruin probability ψ( u) and security coefficient under the condi-tion that the claims obey an exponential distribution or a combination of several exponential distribution and the initial capital is u.

将经典单一型复合 Poisson风险模型推广到带干扰的两险种复合 Poisson-geometric过程。构造调节系数方程并证明了调节系数的存在唯一性之后，运用鞅方法推导出了该风险模型下保险公司破产概率的表达式和破产概率上界，并给出了当个体理赔额服从指数分布时破产概率的表达式。

The classic single type of compound Poisson risk model is extended to two compound Poisson-geometric risk models with interference, an adjustment coefficient equation is constructed, and the existence uniqueness of the adjustment coefficient is proved, the representation and the upper bound of the probability of the ruin of insurance companies are derived using the martingale approach, and finally, the representation for ruin probability is given when individual claims conform to exponential distribution.

讨论了一类一维量子半导体方程,这类方程具有等熵Euler-Poisson方程的形式,并且动量方程有量子势力项和松弛项.当远场动量不一致和远场电场非零时,证明了一维量子Euler-Poisson方程的初值问题的解的渐近性.通过选择适当的修正函数和能量估计的方法,得到了上述初值问题的解在时间足够大时收敛到相应的稳态解.这个结果改进了前人的关于远场动量一致和零远场电场时解的渐近性的结果.

We study the one-dimensional quantum hydrodynamic system for semiconductors. It takes the isentropic Euler-Poisson equations with the quantum potential and momentum relaxation term in the momentum equations. We show the asymptotic behavior of the solutions for the initial value problem to one-dimensional quantum Euler-Poisson equations,when the far field states of the current density are inconsistent and the far field of the electric field is not zero. Choosing proper corrections and using the energy methods, we prove that the solutions of one-dimensional isentropic quantum Euler-Poisson equations decay exponentially fast to the stationary solutions. This result improves previous results in which the current density’s far fields are equal and the far field of the electric field is zero.