风险非同质性保单组合赔付额的计算

对于保单组合赔付次数及赔付额的计算,是非寿险精算研究的一项基本内容.讨论了非同质风险下的保单组合,在赔付次数采用混合泊松分布拟合时的两种情况下赔付额分布的计算,给出了相应的迭代公式.     

总理赔额分布函数的界值及数值计算

根据单个保单理赔额分布函数F(x)的一些特殊性质,研究了开放个别风险模型在保单个数N为负二项分布下,总理赔额分布函数FS(x)对任意x的界值问题,得到一些实用的、便于数值计算的界值结果.     

保单个数为Poisson分布的总理赔额分布函数的界值研究

根据单个保单理赔额分布函数F(z)的一些特殊性质,研究了开放个别风险模型在保单个数N为Poisson分布下,总理赔额分布函数F_S(x)对任意x(x≥0)的界值问题,得到一些实用的、便于数值计算的界值结果,具有重要的应用价值．     

保险精算方法（Ⅱ）

保险精算方法（Ⅱ）严颖成世学程侃二、保单组合索赔总额分布的近似计算２．１概述在个体风险模型中，通常称一组保单为保单组合（ｐｏｒｔｆｏｌｉｏ）。假设此保单组合共含ｎ张保单。考虑一定时段中（如一年）保单组合的索赔总额。记第ｉ张保单的索赔额为Ｘｉ，则保单...     

随机利率下的增额寿险模型研究

在实际的保险精算中,保单保险金现值函数的期望就是该种保单的纯保费,而方差常用来度量该种保单的风险.对随机利率采用W iener过程建模,得到了增额寿险保险金现值函数的期望和方差.     

“清除太空垃圾”是否存在商机呢?

对太空轨道碎片清理的商业运营模式和是否存在商机问题建模进行研究。首先,提出了太空轨道碎片清理公司的商业运营模式,即以清理公司、保险公司和卫星公司为主体的三位一体的系统运营模式;其次,给出私营清理公司商机的定义,通过对运营系统资金费用的分析,定量建立系统正常运营的保险公司最低保单价格和卫星公司最高保险价格求解的模型,并分析了模型的可计算性,给出了商机存在的条件以及商机大小的计算方法;最后,借助于清除效率,建立3种不同轨道碎片清除模式下清除成本的模型,给出了计算不同清除方式下保险公司最低保单价格和卫星公司最高保险价格的模型,验证了定义的商机是合理的并可计算的。     

保费的分析性质及保单的可行性

本文探讨了零效用保费和平均值保费的一些分析性质,并讨论了平均值原理及零效用原理分别作为被保险人及保险人的保费计算原则时,为使保单可行的一个定理,这个定理不仅有较大的理论价值,而且还有一定的实际指导意义。     

带干扰的一类相依风险模型

本文将古典风险模型推广为带干扰的一类相依风险模型。在此风险模型中,保单到达过程为一Pois-son过程,而索赔到达过程为保单到达过程的P-稀疏过程。利用鞅的方法得到了破产概率和Lundberg不等式。     

考虑个体保单风险特征的最优奖惩系统

奖惩系统在汽车保险中的应用非常普遍。论文首先介绍和讨论了泊松-伽马假设下的最优奖惩系统及其性质;其次在假设个体保单的索赔频率服从二项分布,而二项分布的一个参数服从贝塔分布的条件下,建立了一种考虑个体保单风险特征信息的最优奖惩系统,其中风险特征信息可以通过广义线性模型的形式引入奖惩系统;然后在假设个体保单的索赔频率服从负二项分布,而负二项分布的一个参数服从贝塔分布的条件下,建立了另一个最优奖惩系统;最后讨论了这两个奖惩系统的性质和应用。     

最优奖惩系统的构建与评价——基于索赔次数与赔款金额的综合视角

在商业车险中,奖惩系统是一种重要的后验费率调整机制,其基本原理是根据保单的历史索赔信息对续期保费进行调整。常见的奖惩系统仅考虑保单的历史索赔次数信息,但却忽视了赔款金额的影响,这可能会造成产品费率与其实际风险水平不匹配。本文综合考虑保单的索赔次数与赔款金额的信息,利用贝叶斯方法构建了新的最优奖惩系统,并运用极大似然法对模型参数进行估计。本文以我国商业车险中的一组索赔数据为例,进行实证研究。结果表明,对于不同赔款金额的保单,本文所构建的奖惩系统可通过不同的惩罚系数对其续期保费进行调整,从而有效提高后验费率厘定的准确性。     

An optimal portfolio model with stochastic volatility and stochastic interest rate

We consider a portfolio optimization problem under stochastic volatility as well as stochastic interest rate on an infinite time horizon. It is assumed that risky asset prices follow geometric Brownian motion and both volatility and interest rate vary according to ergodic Markov diffusion processes and are correlated with risky asset price. We use an asymptotic method to obtain an optimal consumption and investment policy and find some characteristics of the policy depending upon the correlation between the underlying risky asset price and the stochastic interest rate.     

一种改进的随机次梯度方法的快速收敛性

1引言考虑如下优化问题: min f(x)=sum from i=1 to m f_i(x),s.t. x∈X (1)其中,f_i∶R~n→R是凸函数且f_i不可微,X是R~n上的非空闭凸子集．解(1)的主要方法     

滞后型分段连续随机微分方程的稳定性

本文研究了滞后型分段连续随机微分方程的解析稳定性和数值稳定性问题.首先,利用伊藤公式等方法获得了解析解均方稳定的条件,其次,对于包括均方稳定和T-稳定在内的Euler-Maruyama方法的数值稳定性问题,运用不等式技术和随机分析方法获得了一些新的结果,证明了在一定条件下,Euler-Maruyama方法既是均方稳定又是T-稳定的,推广了随机延迟微分方程的数值稳定性结论.     

个体投资治理污染的随机增长模型

本文研究了个体投资治理污染的随机增长模型.利用随机最优化的方法,得出了随机扰动、个体环保投资及环保技术对福利和经济增长的影响.对我国制定环保政策具有一定的积极作用.     

Q-learning and policy iteration algorithms for stochastic shortest path problems

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in Bertsekas and Yu (Math. Oper. Res. 37(1):66-94, 2012). The main difference from the standard policy iteration approach is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm solves an optimal stopping problem inexactly with a finite number of value iterations. The main advantage over the standard Q-learning approach is lower overhead: most iterations do not require a minimization over all controls, in the spirit of modified policy iteration. We prove the convergence of asynchronous deterministic and stochastic lookup table implementations of our method for undiscounted, total cost stochastic shortest path problems. These implementations overcome some of the traditional convergence difficulties of asynchronous modified policy iteration, and provide policy iteration-like alternative Q-learning schemes with as reliable convergence as classical Q-learning. We also discuss methods that use basis function approximations of Q-factors and we give an associated error bound.     

具有位相型随机补货提前期的PH退化可修系统及其最优更换策略

将几何过程与PH分布相结合, 讨论一个带有位相型随机补货提前期的PH退化可修系统.通过建立最小生成元$Q$矩阵,获得了系统在稳态情形下的状态概率分布向量及其数值解.根据上述研究结果同时也得到了系统的几个重要可靠性指标. 进一步地,还考虑了基于部件故障次数的订购策略和更换策略,导出系统单位时间平均运行成本的解析表达式并给出一个确定最优$N$策略的数值算例.     

Automatic generation of efficient policy alternatives via simulation-optimization

Simulation-optimization methods can be used for many practical and industrial problems in which some or all of the system components are stochastic. These techniques can be applied to a wide variety of problem types, including those in which some functions cannot be represented analytically. In contrast to earlier function optimization approaches, in this paper, these techniques are used for generating several new policy options for planning applications. By using this approach, multiple policy alternatives can be created that meet established system criteria, while simultaneously remaining acceptable and implementable in practice. A subsequent comparative evaluation of the alternatives would be undertaken prior to final policy selection. An illustrative application of the method is provided to demonstrate the usefulness of this approach in the planning phase of policy design.     

约束折扣半马氏决策规划

本文研究约束折扣半马氏决策规划问题，即在一折扣期望费用约束下，使折扣期望报酬达最大的约束最优问题，假设状态集可数，行动集为紧的非空Ｂｏｒｅｌ集，本文给出了ｐ－约束最优策略的充要条件，证明了在适当的假设条件下必存在ｐ－约束最优策略。     

Optimal greedy policies for stochastic control models

We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.     

Optimal resource allocation across related channels

In this paper, we consider resource allocation strategies of a limited resource across two related channels in a multi-period setting. We study a stochastic control problem where the objective is to determine the optimal limited resource allocation policy across two related channels and optimal transshipment policy between these two channels. We characterize some structural results of the optimal resource allocation policy and show that it is determined by three monotone curves.