息力函数综合寿险模型

本以即时给付的综合人寿保险模型为研究对象，考虑到随机利率的影响，用负二项分布和Gamma分布联合建立息力积累函数模型，求出了分期缴费精算现值和给付保险金的精算现值表达式，并可由平衡方程进行保险定价。     

债券定价及利率风险的市场价格的重构方法

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.     

随机期度与利率反向变动关系的初步研究

本文介绍了随机利率下相应的期度—随机期度的定义及其性质.对常见的随机利率模型Vasciek 模型和CIR模型,证明了随机期度与随机利率之间存在着反向的变动关系,从而辅证了随机期度定义的合理性.     

一类随机利率下的增额寿险

寿险中的利率随机问题，是近来保险精算研究的热点和重点问题之一。本以即时给付的一类增额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩。     

An envelope theorem and some applications to discounted Markov decision processes

In this paper, an Envelope Theorem (ET) will be established for optimization problems on Euclidean spaces. In general, the Envelope Theorems permit analyzing an optimization problem and giving the solution by means of differentiability techniques. The ET will be presented in two versions. One of them uses concavity assumptions, whereas the other one does not require such kind of assumptions. Thereafter, the ET established will be applied to the Markov Decision Processes (MDPs) on Euclidean spaces, discounted and with infinite horizon. As the first application, several examples (including some economic models) of discounted MDPs for which the et allows to determine the value iteration functions will be presented. This will permit to obtain the corresponding optimal value functions and the optimal policies. As the second application of the ET, it will be proved that under differentiability conditions in the transition law, in the reward function, and the noise of the system, the value function and the optimal policy of the problem are differentiable with respect to the state of the system. Besides, various examples to illustrate these differentiability conditions will be provided. This work was partially supported by Benemérita Universidad Aut ónoma de Puebla (BUAP) under grant VIEP-BUAP 38/EXC/06-G, by Consejo Nacional de Ciencia y Tecnología (CONACYT), and by Evaluation-orientation de la COopération Scientifique (ECOS) under grant CONACyT-ECOS M06-M01.     

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights,which can be arbi- trarily dependent of each other.Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.     

On an approach to the study of the Jaynes–Cummings sum in quantum optics

A new approach to the study of the Jaynes–Cummings sum, which determines the atomic inversion in quantum model of a single two-level atom interacting with a single mode of the quantized radiation field, based on the number theory theorems on approximation of trigonometric sums is presented.      

Application of the phase‐type mortality law to life contingencies and risk management

The class of phase‐type distributions has recently gained much popularity in insurance applications due to its mathematical tractability and denseness in the class of distributions defined on positive real line. In this paper, we show how to use the phase‐type mortality law as an efficient risk management tool for various life insurance applications. In particular, pure premiums, benefit reserves, and risk‐loaded premiums using CTE for standard life insurance products are shown to be available in analytic forms, leading to efficient computation and straightforward implementation. A way to explicitly determine provisions for adverse deviation for interest rate and mortality is also proposed. Furthermore, we show how the interest rate risk embedded in life insurance portfolios can be analyzed via interest rate sensitivity index and diversification index which are constructed based on the decomposition of portfolio variance. We also consider the applicability of phase‐type mortality law under a few non‐flat term structures of interest rate. Lastly, we explore how other properties of phase‐type distributions may be applied to joint‐life products as well as subgroup risk ordering and pricing within a given pool of insureds. Copyright © 2017 John Wiley & Sons, Ltd.     

循环搜索法在三参数双指数曲面拟合中的应用

在最小二乘意义下用 Gauss-Newton法拟合三参数双指数曲面z =γ[exp( -αx) +exp( -βy) ]时 ,充分利用观测值 ,应用循环搜索法确定了参数初始值 .并成功地以由 Meyer &Roth给出的观测值为例对此进行了验证 .     

库存系统中的时滞变质物品的EOQ模型

本文考虑时段性变质物品的库存问题 .给出了一订货就交货 ,不允许缺货的时滞变质物品的库存模型与最优库存策略 ,并证明了该模型不是那物品自始至终有变质性质的 EOQ模型的简单叠加 .     

Lax等价定理在非线性方面的推广

本文证明了，用差分法求解非线性发展方程的初值问题，当方程适定，在差分格式相容的条件下，稳定性等价于收敛性和逐点Lipschitz条件。从而推广了对线性发展方程成立的Lax等价定理。     

The non-Markovian approach to the valuation and hedging of European contingent claims on power with scaling spikes

We present and further develop a new approach to modeling power prices with spikes proposed earlier by the author. In contrast to other approaches, we model power prices with spikes as a non-Markovian stochastic process that allows for modeling spikes directly as self-reversing jumps. We show how this approach can be used to value European contingent claims on power with spikes as well as to value and dynamically hedge European contingent claims on forwards on power for power with spikes in a practically important special case of the scaling probability distribution for the magnitude of spikes.