强制性约束下企业信息安全投资与网络保险的最优决策分析

研究了强制性约束下企业信息安全投资和网络保险的最优决策问题,对比了可观测企业损失和不可观测企业损失两种情形下基于破产概率约束的最优安全投资和网络保险保费厘定。研究结果表明：在可观测损失和公平保费情况下,当最大化单个企业的期望效用时,存在最优安全投资额,并且政府补贴和强制性约束都可以激励企业增加安全投资;但是当最大化所有企业效用时,只有强制性约束才能增加企业安全投资使得总效用最大化,并且企业的最优安全投资与损失的可观测程度无关。在不可观测损失情况下,当最大化单个企业期望效用时,企业的安全投资增大,而最大化所有企业效用时,存在正网络外部性,即任何企业均不敢轻易的减少安全投资,即使同在一个网络中的其他企业减少了安全投资。此外,在破产概率约束下,随着保费的增加,当损失可观测时,企业的安全投资也增加,但期望效用减少了;而当损失不可观测时,企业的安全投资和期望效用均减少。本文所得结论对政府设定强制性标准,以及企业利用安全投资和网络保险进行信息安全风险控制具有较好的参考价值。     

The Complementary Roles of Mitigation and Insurance in Managing Catastrophic Risks

This paper examines the impact that insurance coupled with specific risk mitigation measures (RMMs) could have on reducing losses from hurricanes and earthquakes as well as improving the solvency position of insurers who provide coverage against these hazards. We first explore why relatively few individuals adopt cost-effective RMMs by reporting on the results of empirical studies and controlled laboratory studies. We then investigate the impact that an RMM has on both the expected losses and those from a worst case scenario in two model cities—Oakland (an earthquake-prone area) and Miami/Dade County (a hurricane-prone area) which were constructed respectively with the assistance of two modeling firms. The paper then explores three programs for forging a meaningful public-private sector partnership: well-enforced building codes, insurance premium reductions linked with long-term loans, and lower deductibles on insurance policies tied to mitigation. We conclude by briefly examining four issues for future research on linking mitigation with insurance.     

The Use of Telematics Devices to Improve Automobile Insurance Rates

Most automobile insurance databases contain a large number of policyholders with zero claims. This high frequency of zeros may reflect the fact that some insureds make little use of their vehicle, or that they do not wish to make a claim for small accidents in order to avoid an increase in their premium, but it might also be because of good driving. We analyze information on exposure to risk and driving habits using telematics data from a pay‐as‐you‐drive sample of insureds. We include distance traveled per year as part of an offset in a zero‐inflated Poisson model to predict the excess of zeros. We show the existence of a learning effect for large values of distance traveled, so that longer driving should result in higher premiums, but there should be a discount for drivers who accumulate longer distances over time due to the increased proportion of zero claims. We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims. We discuss how telematics information can be used to design better insurance and to improve traffic safety.     

Insurance,Public Assistance,and Household Flood Risk Reduction: A Comparative Study of Austria,England, and Romania

In light of increasing losses from floods, many researchers and policymakers are looking for ways to encourage flood risk reduction among communities, business, and households. In this study, we investigate risk‐reduction behavior at the household level in three European Union Member States with fundamentally different insurance and compensation schemes. We try to understand if and how insurance and public assistance influence private risk‐reduction behavior. Data were collected using a telephone survey (n = 1,849) of household decisionmakers in flood‐prone areas. We show that insurance overall is positively associated with private risk‐reduction behavior. Warranties, premium discounts, and information provision with respect to risk reduction may be an explanation for this positive relationship in the case of structural measures. Public incentives for risk‐reduction measures by means of financial and in‐kind support, and particularly through the provision of information, are also associated with enhancing risk reduction. In this study, public compensation is not negatively associated with private risk‐reduction behavior. This does not disprove such a relationship, but the negative effect may be mitigated by factors related to respondents' capacity to implement measures or social norms that were not included in the analysis. The data suggest that large‐scale flood protection infrastructure creates a sense of security that is associated with a lower level of preparedness. Across the board there is ample room to improve both public and private policies to provide effective incentives for household‐level risk reduction.     

The Impact of Mega‐Catastrophes on Insurers: An Exposure‐Based Analysis of the U.S. Homeowners’ Insurance Market

Insurance is a key risk‐sharing mechanism that protects citizens and governments from the losses caused by natural catastrophes. Given the increase in the frequency and intensity of natural catastrophes over recent years, this article analyzes the performance effects of mega‐catastrophes for U.S. insurance firms using a measure of market expectations. Specifically, we analyze the share price losses of insurance firms in response to catastrophe events to ascertain whether mega‐catastrophes significantly damage the performance of insurers and whether different types of mega‐catastrophes have different impacts. The main message from our analysis is that the impact of mega‐catastrophes on insurers has not been too damaging. While the exact impact of catastrophes depends on the nature of the event and the degree of competition within the relevant insurance market (less competition allows insurers to recoup catastrophe losses through adjustments to premiums), our overall results suggest that U.S. insurance firms can adequately manage the risks and costs of mega‐catastrophes. From a public policy perspective, our results show that insurance provides a robust means of sharing catastrophe losses to help reduce the financial consequences of a catastrophe event.     

An agent-based model for evaluating reforms of the National Flood Insurance Program: A benchmarked model applied to Jamaica Bay,NYC

Coastal flood risk is expected to increase as a result of climate change effects, such as sea level rise, and socioeconomic growth. To support policymakers in making adaptation decisions, accurate flood risk assessments that account for the influence of complex adaptation processes on the developments of risks are essential. In this study, we integrate the dynamic adaptive behavior of homeowners within a flood risk modeling framework. Focusing on building-level adaptation and flood insurance, the agent-based model (DYNAMO) is benchmarked with empirical data for New York City, USA. The model simulates the National Flood Insurance Program (NFIP) and frequently proposed reforms to evaluate their effectiveness. The model is applied to a case study of Jamaica Bay, NY. Our results indicate that risk-based premiums can improve insurance penetration rates and the affordability of insurance compared to the baseline NFIP market structure. While a premium discount for disaster risk reduction incentivizes more homeowners to invest in dry-floodproofing measures, it does not significantly improve affordability. A low interest rate loan for financing risk-mitigation investments improves the uptake and affordability of dry-floodproofing measures. The benchmark and sensitivity analyses demonstrate how the behavioral component of our model matches empirical data and provides insights into the underlying theories and choices that autonomous agents make.     

Policy tenure under the U.S. National Flood Insurance Program (NFIP)

In the United States, insurance against flood hazard (inland flooding or storm surge from hurricanes) has been provided mainly through the National Flood Insurance Program (NFIP) since 1968. The NFIP covers $1.23 trillion of assets today. This article provides the first analysis of flood insurance tenure ever undertaken: that is, the number of years that people keep their flood insurance policy before letting it lapse. Our analysis of the entire portfolio of the NFIP over the period 2001-2009 reveals that the median tenure of new policies during that time is between two and four years; it is also relatively stable over time and levels of flood hazard. Prior flood experience can affect tenure: people who have experienced small flood claims tend to hold onto their insurance longer; people who have experienced large flood claims tend to let their insurance lapse sooner. To overcome the policy and governance challenges posed by homeowners' inadequate insurance coverage, we discuss policy recommendations that include for banks and government-sponsored enterprises (GSEs) strengthening their requirements and the introduction of multiyear flood insurance contracts attached to the property, both of which are likely to provide more coverage stability and encourage investments in risk-reduction measures.     

规避农副产品原材料产出不确定风险的商业保险策略

为了保证产品质量、降低生产成本，许多农副产品制造商选择自己种植原材料以满足农副产品的加工生产。然而，农作物的产出易受不利事件（如各种自然灾害）的影响而具有不确定性。这种不确定性可能导致最终产品产出不足，严重时甚至引发财务危机。为了应对潜在风险，农副产品制造商可向金融机构购买商业保险。本文建立了单周期农副产品制造商的计划产量决策模型，通过研究制造商购买商业保险的边界条件及最优商业保险策略，分析商业保险策略在制造商规避原材料产出不确定风险时所具有的价值。研究结果表明：（1）只有保费的安全因子低于外部融资的单位惩罚成本时，制造商才会购买商业保险；（2）最优商业保险策略与计划产量无关；（3）最终产品单位净收益越低，商业保险的价值反而越高。     

A policy lapsation model

Lapsation of a life insurance policy is discontinuation of premium payment by the policy holder during the period of operation of the policy, due to any reason other than the death of the policy holder. The length of life of a lapsed policy can be defined as the period between the month when the last premium instalment was paid and the month the policy was issued. In India, the acceptance of a proposal for life insurance necessitates administrative processes which, together with the agent's commission and medical charges, cost the Life Insurance Corporation almost the whole of the first year's and a major part of the second year's premium. Early lapses, therefore, pose a major financial problem to the Corporation. In this study, the pattern of early policy lapses was empirically investigated with a view to formulating a model for the lapsation phenomenon. It has been realized that the phenomenon is not amenable to any simple statistical model due to an inherent stratification in the population of lapsed policies.     

Cyber Security Risk Management: Public Policy Implications of Correlated Risk,Imperfect Ability to Prove Loss,and Observability of Self‐Protection

The correlated nature of security breach risks, the imperfect ability to prove loss from a breach to an insurer, and the inability of insurers and external agents to observe firms’ self‐protection efforts have posed significant challenges to cyber security risk management. Our analysis finds that a firm invests less than the social optimal levels in self‐protection and in insurance when risks are correlated and the ability to prove loss is imperfect. We find that the appropriate social intervention policy to induce a firm to invest at socially optimal levels depends on whether insurers can verify a firm's self‐protection levels. If self‐protection of a firm is observable to an insurer so that it can design a contract that is contingent on the self‐protection level, then self‐protection and insurance behave as complements. In this case, a social planner can induce a firm to choose the socially optimal self‐protection and insurance levels by offering a subsidy on self‐protection. We also find that providing a subsidy on insurance does not provide a similar inducement to a firm. If self‐protection of a firm is not observable to an insurer, then self‐protection and insurance behave as substitutes. In this case, a social planner should tax the insurance premium to achieve socially optimal results. The results of our analysis hold regardless of whether the insurance market is perfectly competitive or not, implying that solely reforming the currently imperfect insurance market is insufficient to achieve the efficient outcome in cyber security risk management.     

Robustness of Optimal Investment Decisions in Mixed Insurance/Investment Cyber Risk Management

An integrated risk management strategy, combining insurance and security investments, where the latter contribute to reduce the insurance premium, is investigated to assess whether it can lead to reduced overall security expenses. The optimal investment for this mixed strategy is derived under three insurance policies, covering, respectively, all the losses (total coverage), just those below the limit of maximum liability (partial coverage), and those above a threshold but below the maximum liability (partial coverage with deductibles). Under certain conditions (e.g., low potential loss, or either very low or very high vulnerability), the mixed strategy reverts however to insurance alone, because investments do not provide an additional benefit. When the mixed strategy is the best choice, the dominant component in the overall security expenses is the insurance premium in most cases. Optimal investment decisions require an accurate estimate of the vulnerability, whereas larger estimation errors may be tolerated for the investment-effectiveness coefficient.     

Defined contribution health care: future direction or fantasy?

Will payers embrace defined contribution plans as an alternative to traditional health insurance or is this new approach a pipe dream? Are consumers truly ready to make informed decisions on purchasing their own health care? This article explores barriers to defined contribution health plans, including consumer reluctance to take ownership of buying insurance and a preference for the cost predictability of liberal coverage in employer-sponsored programs versus MSAs or higher co-payment arrangements. For the ultimate form of defined contribution health care to work, several tax and insurance barriers must be overcome. As a practical matter, the author argues that the current employer-sponsored approach is the most efficient system for large employers.     

Insurance Policies for Monetary Policy in the Euro Area

In this paper, we aim to design a monetary policy for the euro area that is robust to the high degree of model uncertainty at the start of monetary union and allows for learning about model probabilities. To this end, we compare and ultimately combine Bayesian and worst‐case analysis using four reference models estimated with pre–European Monetary Union (EMU) synthetic data. We start by computing the cost of insurance against model uncertainty, that is, the relative performance of worst‐case or minimax policy versus Bayesian policy. While maximum insurance comes at moderate costs, we highlight three shortcomings of this worst‐case insurance policy: (i) prior beliefs that would rationalize it from a Bayesian perspective indicate that such insurance is strongly oriented towards the model with highest baseline losses; (ii) the minimax policy is not as tolerant towards small perturbations of policy parameters as the Bayesian policy; and (iii) the minimax policy offers no avenue for incorporating posterior model probabilities derived from data available since monetary union. Thus, we propose preferences for robust policy design that reflect a mixture of the Bayesian and minimax approaches. We show how the incoming EMU data may then be used to update model probabilities, and investigate the implications for policy. (JEL: E52, E58, E61)     

二维GPSJ分布类及其在保险中的应用

本文给出的二维GPSJ分布类(即GPSJ2)在保险领域应用范围较广,如由机动车辆保险由财产损失索赔次数和人身伤亡索赔次数所组成的模型、超额再保险中的由自留保单数和分出报单数所组成的二维模型等。本文在GPSJ1类基础上研究二维GPSJ类,本文给出了此分布类的定义、背景意义、概率计算的递推公式,同时还对各参数的最大似然估计值的求解过程进行了分析。本文最后将这一模型应用于一组机动车辆赔付次数数据,考虑了由财产损失索赔次数、人身伤亡索赔次数组成的二维模型,拟合效果令人满意。     

基于有理样条死亡假设的分数时点寿险净保费责任准备金

保险责任准备金是保险公司风险管理的重要度量指标,责任准备金的精确合理的测算,将会对保险公司的健康发展起着极其重要的作用。分数时点净保费责任准备金的测算依赖于精算假设,本文在提出一类有理样条死亡假设的基础上,研究了终身寿险的分数时点净保费责任准备金的计算问题。我们得到了其理论计算公式和上下界范围,探讨了调节参数的变化对净保费责任准备金的影响。数据分析表明:分数时点责任准备金对调节参数的变化比较敏感,目前常用的UDD假设下的责任准备金测算值恰是本文方法下的一个边界。所以基于有理样条估计方法的分数时点责任准备金测算在实务中具有很强的灵活性,对保险公司责任准备金风险管理具有重要的指导意义。     

电子商务产品定价与返利策略优化及协调研究

在电子商务背景下,网络零售商以两种模式向消费者提供产品,一种是常规的网络直销模式,另一种是通过有第三方返利平台参与的返利模式.当两种模式同时存在时,利用消费者效用理论,分别研究了网络零售商的最优定价策略与第三方返利平台的最优返利策略.结果表明,网络零售商是否引入返利模式,与返利产品的满足率、消费者购买返利产品花费的额外成本及返利兑现率密切相关.相对于集中式决策,分散式决策下网络零售商的最优零售价格会降低,同时第三方返利平台返还给消费者的返利会减少,这会加剧两种模式之间的冲突而导致系统低效率.为此,设计了一种改进的收益共享合同来协调两种销售模式,不仅使系统效率达到最优,并且使渠道成员实现"共赢".最后结合数值算例验证了该合同的有效性.     

Are People Willing to Buy Natural Disaster Insurance in China? Risk Awareness,Insurance Acceptance,and Willingness to Pay

After the Wenchuan earthquake (magnitude 7.9, May 12, 2008), intensive debates on how China should establish a natural disaster insurance system were initiated among researchers, policymakers, and insurance professionals. Our focus was the social aspects of disaster insurance, explored in China through a nationwide survey. Our questionnaires investigated people's risk awareness, insurance acceptance, their opinions on governmental measures for disaster management, and their willingness to pay for disaster house insurance. We analyzed the results at both regional and individual scales. We found that the integrated hazard index and respondents’ experience of insurance (considered objective factors), and their opinions on the importance of insurance and government responsibility (considered subjective factors) showed strong correlation with the regional overall acceptance of disaster insurance. An individual's decision to participate highly depended on his/her experience of both insurance and disaster and his/her opinion on the importance of insurance as a coping mechanism. Respondents from poverty‐stricken or less‐developed counties were not necessarily more reluctant to accept natural disaster insurance, though they exhibited relatively lower ability to afford insurance. In general, respondents had correct perceptions of natural disasters in their areas; however, people from regions with a greater multihazard threat showed less willingness to accept disaster insurance because they tended to expect the government to undertake to cover losses and considered insurance to be less important. People's willingness to pay for an assumed disaster house insurance was also investigated and analyzed. We consequently discuss the policy implications for developing a disaster insurance system in China.     

执行时间视角下的可再生能源发电项目激励政策优化研究

为实现可持续发展并降低温室气体排放,中国需大力发展可再生能源,而激励政策对可再生能源发展具有重要推动作用。鉴于此,本文采用实物期权方法评价了中国可再生能源发电项目激励政策的实施效果：首先分析了可再生能源项目的经济性,提出模型假设,接着构建并求解实物期权模型。为更直观地评价激励政策效果,本文利用最优执行条件求解项目预期执行时间和不同技术水平下的激励政策最优值。最后,以光伏发电项目为例进行实证分析。研究表明：①目前,中国光伏产业还难以独立发展,仍需国家政策的支持,但现行或曾实施的光伏激励政策存在超额激励现象。②随着技术水平的提高,为鼓励投资者及时投资,政府需提高激励力度。③从政府支出、政策效果和技术影响三个角度综合分析,单项激励政策中上网电价政策效果最佳,但政府支出较高;价格补贴政策效果偏弱,但政府支出较低;与其他两项政策相比,成本补偿政策效果较差。     

随机组合风险的风险溢价

随机组合风险在保险索赔理论、金融及经济管理等领域有广泛的应用,数学上采用随机和来刻画随机组合风险。风险溢价在金融经济学及保险经济学的理论中都是很重要的概念,它不仅与风险的大小有关,还与当事人对风险的态度有关,从理论上看就是与当事人的效用函数有关。本文研究在期望效用理论下随机组合风险的风险溢价问题,探讨了由组合数(如索赔次数)的不确定性所引起的风险溢价,给出了几种不同效用函数下随机组合风险的风险溢价的计算公式,并特别针对随机Poisson组合及随机Poisson-Geometric组合给出了其风险溢价的计算公式及性质。     

Manufacturer Rebate Competition in a Supply Chain with a Common Retailer

We consider manufacturer rebate competition in a supply chain with two competing manufacturers selling to a common retailer. We fully characterize the manufacturers’ equilibrium rebate decisions and show how they depend on parameters such as the fixed cost of a rebate program, market size, the redemption rate of rebate, the proportion of rebate‐sensitive consumers in the market and competition intensity. Interestingly, more intense competition induces a manufacturer to lower rebate value or stop offering rebate entirely. Without rebate, it is known that more intense competition hurts the manufacturers and benefits the retailer. With rebate, however, more intense competition could benefit the manufacturers and hurt the retailer. We find similar counterintuitive results when there is a change in some other parameters. We also consider the case when the retailer subsidizes the manufacturers sequentially to offer rebate programs. We fully characterize the retailer's optimal subsidy strategy, and show that subsidy always benefits the retailer but may benefit or hurt the manufacturers. When the retailer wants to induce both manufacturers to offer rebate, he always prefers to subsidize the manufacturer with a higher fixed cost first. Sometimes the other manufacturer will then voluntarily offer rebate even without subsidy.