Long-Term Care Insurance and Life Insurance Demand

This article investigates the interaction between life insurance and long-term care insurance markets on the demand side. In the model utility depends on both consumption and bequest, and utility from consumption is contingent on the state of health. While the demand for life insurance increases both with decreasing income and with a rising degree of altruism, the influences of these two parameters on the demand for long-term care insurance are ambiguous. If the utility shock arising from disability declines, both insurance demands will rise.     

Long-Term Care Insurance Purchase Patterns

Given the aging population and high cost of long-term care, many Americans are concerned about financing long-term care services. Despite this concern, private long-term care insurance policy sales have experienced slow growth. On average only about 7 percent of the population aged 65 and older has long-term care insurance, but this percentage varies greatly across the states. In this study we test hypothesized relationships between purchase of long-term care insurance and various explanatory factors. We provide evidence that state Medicaid nursing home expenditure levels and the relative sizes of the elderly population and the nursing home population are significant explanatory factors of purchase rates. We find no evidence that public–private partnership regulation, the quality of available facilities, or agent marketing controls affect purchase. Findings of the study are useful to insurers, legislators, regulators, and others involved in the public policy debate about financing long-term care.     

Narrow Framing and Long-Term Care Insurance

We propose a model of narrow framing in insurance and test it using data from a new module we designed and fielded in the Health and Retirement Study. We show that respondents subject to narrow framing are substantially less likely to buy long-term care insurance than average. This effect is much larger than the effects of risk aversion or adverse selection, and it offers a new explanation for why people underinsure their later-life care needs.     

Predictive Modeling in Long-Term Care Insurance

The accurate prediction of long-term care insurance (LTCI) mortality, lapse, and claim rates is essential when making informed pricing and risk management decisions. Unfortunately, academic literature on the subject is sparse and industry practice is limited by software and time constraints. In this article, we review current LTCI industry modeling methodology, which is typically Poisson regression with covariate banding/modification and stepwise variable selection. We test the claim that covariate banding improves predictive accuracy, examine the potential downfalls of stepwise selection, and contend that the assumptions required for Poisson regression are not appropriate for LTCI data. We propose several alternative models specifically tailored toward count responses with an excess of zeros and overdispersion. Using data from a large LTCI provider, we evaluate the predictive capacity of random forests and generalized linear and additive models with zero-inflated Poisson, negative binomial, and Tweedie errors. These alternatives are compared to previously developed Poisson regression models.

Our study confirms that variable modification is unnecessary at best and automatic stepwise model selection is dangerous. After demonstrating severe overprediction of LTCI mortality and lapse rates under the Poisson assumption, we show that a Tweedie GLM enables much more accurate predictions. Our Tweedie regression models improve average predictive accuracy (measured by several prediction error statistics) over Poisson regression models by as much as four times for mortality rates and 17 times for lapse rates.     

夫妻联合长期护理保险的定价模型与应用

在人口老龄化和人口长寿背景下,社会对老年长期护理保障的需求不断增长,基于家庭保障的理念,本文将多元寿险模型推广到夫妻联合长期护理保险,构建了健康、轻度失能、重度失能和死亡的马尔科夫四状态转移模型,并在联合个体状态转移相互独立的假设下给出了夫妻联合长期护理保险定价模型.最后基于中国老年健康影响因素跟踪调查微观数据,实现了...     

The Profitability and Pricing of Major Customers

We examine the profitability and valuation of retail firms identified by suppliers as major customers, using major customer relationships to proxy for unrecorded organizational-capital intangibles. Major customers have higher operating profitability and profitability persistence, with the sources of the higher profitability consistent with purported advantages of supply chain arrangements. The pricing of major customers is consistent with the market recognizing the level and over-time properties of operating profitability. Together, these results suggest that investors understand the profitability effects of unrecorded organizational intangible assets and that financial statement analysis can be used to further examine the valuation effects of such intangibles.     

长期护理保险的理论研究:进展与前景

随着中国步入老龄化社会、家庭结构小型化和空巢家庭增加,导致了传统家庭养老模式的转变,老年人对专业化护理的需求日益增长。长期护理状态发生的不确定性以及专业护理费用的攀升,使得长期护理风险愈加突出,并将成为一种重要的社会风险。因此,开发长期护理保险产品在我国存在巨大的市场空间。本文从长期护理保险的需求、定价以及运作模式等方面回顾了国内外长期护理保险的理论研究进展,同时提出了需要进一步研究的领域和方向。     

Issuance Decisions and Strategic Focus: The Case of Long-Term Care Insurance

Increasing costs of long-term care are placing ever greater burdens on state and federal budgets, yet private long-term care insurance remains a relatively minor financing vehicle. Although many researchers provide rationales for the limited private market, some life–health insurers have forged ahead into this relatively new and risky line of business. We investigate what makes these insurers different and whether managers are following a diversification or strategic focus strategy. We find that strategic focus is a consistently important factor and that managers' participation and volume decisions are made independently.     

日本长期护理保险制度发展方向及对我国的启示

随着我国老龄化程度日益加深,需要长期护理服务的失能老年人数急剧攀升,构建高效的长期护理保险制度已迫在眉睫。经过10多年的发展,日本长期护理保险制度已十分成熟。本文通过对日本长期护理保险制度的研究,总结出社会性长期护理保险制度的优势和不足,为我国构建可持续发展的长期护理保险制度提供启示。从日本的经验得出,我国应构建社会性性长期护理保险与商业性长期护理保险相结合的长期护理保险制度,以期同时实现广覆盖、保障性、资金筹集方式多元化与保单形式多样化等目标。     

An Insurance Pricing Game

Understanding data and statistical distributions is a fundamental part of an undergraduate business student's education. The insurance pricing game presented here gives the students a unique way to apply statistical analysis in the classroom. The game requires decision making about risk with limited information. Specifically, the students must decide what “premium” to charge the members of a hypothetical risk pool. The game provides teachers with a discussion platform for numerous aspects of insurer risk pooling.     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

Cybersecurity Insurance: Modeling and Pricing

Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this study, we develop a framework for modeling and pricing cybersecurity risk. The proposed model consists of three components: the epidemic model, loss function, and premium strategy. We study the dynamic upper bounds for the infection probabilities based on both Markov and non-Markov models. A simulation approach is proposed to compute the premium for cybersecurity risk for practical use. The effects of different infection distributions and dependence among infection processes on the losses are also studied.     

Asymmetric Information, Long-Term Care Insurance, and Annuities: The Case for Bundled Contracts

This article examines the markets for long-term care insurance and annuities when there is asymmetric information and there are costs of administering contracts. Individuals differ in terms of their risk aversion. Risk-averse individuals take more care of their health and are relatively high risk in the annuities market and relatively low risk in the long-term care insurance market. In the long-term care insurance market, both separating and partial-pooling equilibria are possible. However, in the stand-alone annuity market, only separating equilibria are possible. We show, consistent with the extant empirical research, that in the presence of administration costs the more risk-averse individuals may buy relatively more long-term care insurance and more annuity coverage. Under the same assumptions, we show that equilibria exist with bundled contracts that Pareto dominate the outcomes with stand-alone contracts and are robust to competition from stand-alone contracts. The remaining empirical puzzle is to explain why bundled contracts are such a small share of the voluntary annuity market.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

Fuzzy Financial Pricing of Property-Liability Insurance

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.     

社保模式下实物给付型长期护理保险发展瓶颈及对策

伴随着相关政策的出台,社保模式下的长期护理保险制度逐渐浮出水面,并在各试点地区开始尝试实物给付型长期护理保险,以满足消费者多层次、多样化的需求。随着老年人护理需求和意愿不断增长,长期护理保险的市场需求正在逐步扩大。但是,和巨大的潜在市场需求相比,长期护理保险市场的供给相对缺失,试点实践中存在给付方式单一、法律法规缺失、筹资机制不完善、护理设施及资源不足等诸多问题。借鉴国外经验,本文针对以上问题提出了完善建议,以期为我国社保模式下实物给付型长期护理保险的发展提供可鉴思路。     

存款保险定价研究:期权定价法和预期损失定价法的进展

合理的存款保险定价可有效减少道德风险和逆向选择问题。本文梳理了国内外关于存款保险定价的两种主要方法——期权定价法和预期损失定价法及其最新发展情况。期权定价法的核心是将存款保险看作存款保险机构以银行资产为标的发行的一份看跌期权,之后学者从股利发放、监管宽容、系统性风险等多个角度进行拓展。预期损失定价法主要根据边际损失与边际保费收入相等来进行保费厘定,以探寻如何通过更科学的方法更精确地测量银行的预期损失。此外,本文讨论了存款保险定价方法对我国的启示。