Optimal Insurance with Background Risk under the Ambiguity and Belief Heterogeneity Structure

In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal insurance contract when maxing the insured’s expected utility of his/her remaining wealth under the smooth ambiguity model and the heterogeneous belief form satisfying the MHR condition. We calculate the insurance premium by using generalized Wang’s premium and also introduce a series of stochastic orders proposed by [1] to describe the relationships among the insurable risk, background risk and ambiguity parameter. We obtain the deductible insurance is the optimal insurance while they meet specific dependence structures.

Engineering models for catastrophe risk and their application to insurance

Internationally earthquake insurance,like all other insurance (fire,auto),adopted actuarial approach in the past, which is,based on historical loss experience to determine insurance rate.Due to the fact that earthquake is a rare event with severe consequence,irrational determination of premium rate and lack of understanding scale of potential loss led to many insurance companies insolvent after Northridge earthquake in 1994. Along with recent advances in earth science,computer science and engineering,computerized loss estimation methodologies based on first principles have been developed to the point that losses from destructive earthquakes can be quantified with reasonable accuracy using scientific modeling techniques. This paper intends to introduce how engineering models can assist to quantify earthquake risk and how insurance industry can use this information to manage their risk in the United States and abroad.

Ruin Probability of One Kind of Entrance Processes Based Insurance Risk Models

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.

Evolution of seismic risk management for insurance over the past 30 years

During the past 30 years, there has been spectacular growth in the use of risk analysis and risk management tools developed by engineers in the financial and insurance sectors. The insurance, the reinsurance, and the investment banking sectors have enthusiastically adopted loss estimation tools developed by engineers in developing their business strategies and for managing their financial risks. As a result, insurance/reinsurance strategy has evolved as a major risk mitigation tool in managing catastrophe risk at the individual, corporate, and government level. This is particularly true in developed countries such as US, Western Europe, and Japan. Unfortunately, it has not received the needed attention in developing countries, where such a strategy for risk management is most needed. Fortunately, in the last five years, there has been excellent focus in developing ＂Insur Tech＂ tools to address the much needed ＂Insurance for the Masses＂, especially for the Asian Markets. In the earlier years of catastrophe model development, risk analysts were mainly concerned with risk reduction options through engineering strategies, and relatively little attention was given to financial and economic strategies. Such state-of-affairs still exists in many developing countries. The new developments in the science and technologies of loss estimation due to natural catastrophes have made it possible for financial sectors to model their business strategies such as peril and geographic diversification, premium calculations, reserve strategies, reinsurance contracts, and other underwriting tools. These developments have not only changed the way in which financial sectors assess and manage their risks, but have also changed the domain of opportunities for engineers and scientists.This paper will address the issues related to developing insurance/reinsurance strategies to mitigate catastrophe risks and describe the role catastrophe risk insurance and reinsurance has played in managing financial risk due to natural catastrophes. Historical losses and the share of those losses covered by insurance will be presented. How such risk sharing can help the nation share the burden of losses between tax paying public, the ＂at risk＂ property owners, the insurers and the reinsurers will be discussed. The paper will summarize the tools that are used by the insurance and reinsurance companies for estimating their future losses due to catastrophic natural events. The paper will also show how the results of loss estimation technologies developed by engineers are communicated to the business flow of insurance/reinsurance companies. Finally, to make it possible to grow ＂Insurance for the Masses - IFM＂, the role played by parametric insurance products and Insur Tech tools will be discussed.

The Finite-time Ruin Probability of a Discrete-time Risk Model with Subexponential and Dependent Insurance and Financial Risks

Consider a discrete-time risk model with insurance and financial risks in a stochastic economic environment. Assume that the insurance and financial risks form a sequence of independent and identically distributed random vectors with a generic random vector following a wide type of dependence structure. An asymptotic formula for the finite-time ruin probability with subexponential insurance risks is derived. In doing so, the subexponentiality of the product of two dependent random variables is investigated simultaneously.

风险约束与最优保险:一种更符合投保人期望的保险契约

在保险实践中,投保人往往期望在发生保险事故之后能够获得保险公司的充分赔偿,从而确保他们的实际经济损失被严格控制在预先设定的、可接受的阈值之内。为了满足这类保险需求,本文考虑当投保人损失不大于某个非负特定值时,在Arrow模型的基础上引入投保人的净损失约束以研究投保人的最优保险问题。具体的,本文在投保人的低损失区间而非全损失、高损失区间引入净损失约束,既考虑了投保人效用的帕累托改进,同时又使最优保单含有对投保人合理避险的激励。研究表明:投保人效用最优时,如果低损失区间上的净损失约束不起作用,则Arrow模型解就是本模型的解;反之如果起到作用,则给出了本模型的一个特殊解,并且指出该特殊解存在两个免赔额。此外,投保人的期望效用会随着净损失上限的增大和小损分界点的减小而有所提高,但当净损失上限增大或小损分界点减小到一定程度使得投保人低损失区间上的净损失约束不起作用时,投保人效用达到最大而不再进一步提高。

我国老年失能风险研究:基于删失数据半参转换模型

老年失能风险是人口老龄化背景下值得关注的重要问题。已有研究往往忽略失能数据的删失属性,因而无法充分利用数据信息。本文提出了一种新的老年失能风险建模方法,在考虑失能数据区间删失和右删失的情况下,对中国老年健康影响因素跟踪调查(CLHLS)数据按个体从健康状态转移到首次失能状态经历的时间进行分类,同时利用CLHLS死亡调查补充个体死亡前的失能信息。在此基础上,基于生存分析中的半参数转换失能时间模型,实现对老年失能率更准确的估计和预测。与传统模型相比,新模型将年龄、性别、教育水平等变量纳入模型,能够对不同特征人群的失能风险做更细致和精准的分析,为完善我国长期护理保险制度提供实证依据。

Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

Precise large deviation result for heavy-tailed random sums and applications to risk theory

The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.

临床预测模型在医保付费中的应用前景探索

推进医保支付方式改革是医保高质量发展的需要,更是减轻人民群众就医负担、增进民生福祉的需要。近年来,我国多元复合式医保支付方式改革取得积极进展,同时也对医保基金管理和医疗机构管理提出了更高要求。在医疗健康大数据背景下,临床预测模型被成熟应用于药物试验等领域,在量化评估患者所患疾病风险程度、医疗资源消耗强度等方面展现出较好的能力。本文旨在借鉴医保风险调整机制和风险预测模型相关国际经验,研究临床预测模型应用于医保支付方式改革下疾病诊断相关分组和医保偿付风险调整的可行性,为进一步提高医疗机构服务质量,提升医保基金使用效能提供参考。

我国苹果主产区“保险+期货”模式运行机制与发展建议

“保险+期货”模式是我国农业领域的创新型风险管理工具,也是农业保险高质量发展方向的旗帜,更是保障农业生产者收益的可靠手段。目前“保险+期货”模式多应用于小麦等粮食作物,对于苹果等经济作物的探索仍在初始阶段。文章介绍了“保险+期货”的两种模式,梳理了当前我国各苹果主产地区实行“保险+期货”模式的现状,并指出了存在的问题,据此提出了扩大试点范围、建立信息共享和培训体系、加大政府财政补贴支持力度等建议,从而为我国其他经济类农产品的“保险+期货”模式试点提供可借鉴的路径。

基于风险调整模型的医保用户在线DRG支付系统设计

为提升医保用户在线DRG支付效果,使在线支付更加便捷有效,提出一种基于风险调整模型的医保用户在线DRG支付系统。基于系统的总体架构,设计中央控制器和嵌入式开发板等硬件部分,为实现系统软件模块奠定基础,采用风险特征模型对DRG分组的风险因素进行分析,通过计算用户交易行为的安全水平与支付信息价值,对用户支付过程进行加密处理,结合支付管理模块与数据库完成系统软件的设计。系统性能测试结果表明,设计的系统能够更快速地处理支付交易业务,处理效率较高,具有一定应用价值。

基于财务共享模式下保险公司内部控制优化研究

财务共享模式在保险公司内部控制中具有重要作用。本研究通过分析财务共享的特点,探讨了其对内部控制的影响,并深入剖析了保险公司在财务共享模式下存在的内部控制问题。在此基础上,提出了一系列优化对策,以提升业务与财务融合度、完善人力资源管理机制、优化财务共享风险评估管理机制、优化财务共享内部控制活动、以及优化财务共享信息沟通机制。通过实施这些对策,可以有效提高保险公司内部控制的效能和水平。

Applications of Mogulskii, and Kurtz-Feng Large Deviation Results to Risk Reserve Processes with Aggregate Claims

In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions including (the non-super- exponential) exponential claims. We prove two large deviations principles: first, we obtain the LDP for risk processes on D∈[0,1] with the Skorohod topology. In this case, we provide an explicit form for the rate function, in which the safety loading condition appears naturally. The second theorem allows us to obtain the LDP for Aggregate Claims processes on D∈[0,∞) with a different time-scale modification. As an application of the first result we estimate the ruin probability, and for the second result we work explicit calculations for the case of exponential claims.

Study of Volatility Stochastic Processes in the Context of Solvency Forecasting for Sri Lankan Life Insurers

The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.

推进风险模型系统建设,强化农业保险的风险管理

农业风险管理体系的建立是中国农业产业稳定发展的重要基石。农业保险作为重要的农业风险管理工具,正在从单一赔付服务向全流程农业风险管理转型。构建农业风险模型,研发农业风险模型系统,实现农业风险的自动化和智能化模拟、计算与决策,对提升农业风险识别、分析、评估、预测和决策能力,实现农业保险的风险管理转型升级具有重要意义。在归纳总结农业风险与风险模型的基础上,对农业风险模型系统的应用价值和建设路径进行深入分析,列举现阶段中国农业风险模型系统的典型案例,分析指出了现阶段存在的问题,并提出了推进中国农业风险模型系统建设、为强化农业保险风险管理提供重要支撑的建议。

“后脱贫时代”基于早逝风险的保险扶贫效应研究

保险凭借其独特的优势被广泛应用于扶贫工作中,本文选择早逝风险为切入点,首先分析了我国早逝风险的现状,然后基于多重均衡模型分别构建不包含人寿保险和包含人寿保险的家庭投资消费决策模型,之后利用保险相关数据开展数值模拟,得到不同初始资产水平下家庭资产随时间演变路径以及陷贫概率。研究发现,人寿保险的扶贫效应与家庭初始资产水平有关:只有当家庭资产高于某一阈值时,人寿保险才能够有效缓解家庭因为劳动力早逝而出现的贫困风险,否则甚至可能加剧风险。敏感性分析发现,扶贫效应随着保险金额的增大而增大,随着损失率的降低而相对增强。当损失率较高时,购买人寿保险并不能完全摆脱贫困风险,但确实在一定程度上降低了陷贫概率;随着损失率的降低,人寿保险扶贫方面的相对作用增强,陷贫概率甚至降至零。本文为保险业助力巩固脱贫成果、护航乡村振兴、实现共同富裕提供了理论指导,特别是家庭有必要在保险给付后的“保护期”,尽快将保险金额转化为生产要素,这样才能从根本上摆脱“返贫”问题。

高保障水平农业保险对新种子技术采纳行为的影响

高保障水平农业保险能够通过其风险保障功能缓解农户对风险的担忧,进而加强农户对新种子技术的采纳。该文基于对内蒙古自治区玉米种植户的问卷调查数据,运用Probit模型,以完全成本保险这一典型高保障水平农业保险为例,识别其对农户新种子技术采纳行为的影响作用,同时关注农户的风险担忧状况对新种子技术采纳行为产生的影响。结果表明,高保障水平的农业保险能够增强农户对新种子技术的采纳行为;风险担忧程度越低的农户越倾向采用新种子技术;以及农户的风险担忧在高保障水平农业保险对农户新种子技术采纳行为的作用路径中发挥部分中介效应。最后该文从制定差异化保险方案,发挥社会网络互助作用以及支持青年劳动力返乡就业等方面提出政策启示。

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 arbitrarily dependent of each other. Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.