投保人异质性风险偏好下指数保险市场均衡的动态演化分析

兼具道德风险与逆向选择免疫性和即刻赔付双重优势的指数保险逐渐成为巨灾风险管理的重要工具,但目前多处于试点阶段,市场均衡演化规律仍不明确。本文构建了指数保险市场中保险公司、投保人和政府的三方演化博弈模型,同时,考虑投保人面对损失与收益的不同风险态度,引入异质性风险偏好设计了投保人决策函数,进而分析指数保险市场均衡演化路径及其影响因素。结果表明,指数保险市场均衡随其生命周期的演进而变化,政府在指数保险市场中的职能将从管理者走向退出;政府对保险公司进行补贴更有效,但补贴力度需在适度范围内。影响因素方面,投保人的异质性风险偏好对市场均衡演化有重要影响,其损失敏感性将加快市场向均衡状态的收敛速度;提前赔付优势能够促进市场向均衡状态收敛,但溢出效应会延缓均衡的达成。基于此提出了政府对指数保险市场引导与鼓励的建议。     

Simulation of a health insurance market with adverse selection

A health insurance market is examined in which individuals with a history of high utilization of health care services tend to select fee-for-service (FFS) insurance when offered a choice between FFS and health maintenance organizations (HMOs). In addition, HMOs are assumed to practice community rating of employee groups. Based on these observations and health plan enrollment and premium data from Minneapolis-St. Paul, a deterministic simulation model is constructed to predict equilibrium market shares and premiums for HMO and FFS insurers within a firm. Despite the fact that favorable selection enhances their ability to compete with FFS insurers, the model predicts that HMOs maximize profits at less than 100% market share, and at a lower share than they could conceivably capture. That is, HMOs would not find it to their advantage to drive FFS insurers from the market even if they could. In all cases, however, the profit-maximizing HMO premium is greater than the experience-rated premium and, thus, the average health insurance premium per employee in firms offering both HMOs and FFS insurance is predicted to be greater than in firms offering one experience-rated plan. The model may be used to simulate the effects of varying the employer's method of contributing to health insurance premiums. Several contribution methods are compared. Employers who offer FFS and HMO insurance and pay the full cost of the lowest-cost plan are predicted to have lower average total premiums (employer plus employee contributions) than employers who pay any level percent of the cost of each plan.     

Competitive insurance pricing with complete information,loss-averse utility and finitely many policies

In a recent paper, Ramsay and Oguledo (2012) show that in a competitive insurance market with complete information about individuals’ accident probabilities and production costs, which are proportional to the amount of insurance purchased and to the premium charged, only individuals whose accident probability is in a medium range are insurable and desire insurance. The purpose of this paper is to complement the analysis of Ramsay and Oguledo by considering production costs which are proportional to the number of policies offered by an insurer. In addition to the result of Ramsay and Oguledo we show that the group of individuals who obtain insurance is partitioned into several subgroups, where each subgroup is offered the same insurance policy. To derive this result we introduce the concept of incentive compatibility which ensures that an individual has no incentive to buy another policy. Assuming that individuals have loss-averse utility, we fully characterize the boundaries of these subgroups as the result of an undercutting process in premiums between the insurers.     

Competitive insurance market in the presence of ambiguity

Within the context of a competitive insurance market, this paper examines the impact of ambiguity on the behavior of buyers and sellers. Ambiguity is described through a probability measure on an extended state space that includes extra ambiguous states. It is shown that if insurers face the same or less ambiguity than their customers, a unique equilibrium exists where customers are fully insured. On the other hand, if insurers face more ambiguity than their customers, customers will be under insured and it is even possible that customers may not purchase any insurance.     

Reexamining the feasibility of diversification and transfer instruments on smoothing catastrophe risk

The present study discusses the effects of diversification and transfer of risk by global insurers on smoothing the peak of catastrophic claims. Empirical experiments indicate that the occurrence frequency of natural catastrophes (NatCat) has a serially dependent trend and that the Cox–Ingersoll–Ross square-root model for global insured losses is best fit than any other static distributions. The results are used to develop a NatCat risk insurance model that sets up a NatCat premium formula, uses the serially dependent dynamics of insured loss and establishes the cash flow of all involved parties while considering corporate income tax and no additional risk premium. The simulation results based on this model shows that fluctuation reserves, catastrophe bonds and catastrophe funds with payback schemes are feasible options for smoothing risk because they can benefit all long-term involved parties, including insurance company shareholders, the insured, bondholders, the fund and the government (i.e. taxpayers).     

A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers

In this work, we study the equilibrium reinsurance/new business and investment strategy for mean–variance insurers with constant risk aversion. The insurers are allowed to purchase proportional reinsurance, acquire new business and invest in a financial market, where the surplus of the insurers is assumed to follow a jump–diffusion model and the financial market consists of one riskless asset and a multiple risky assets whose price processes are driven by Poisson random measures and independent Brownian motions. By using a version of the stochastic maximum principle approach, we characterize the open loop equilibrium strategies via a stochastic system which consists of a flow of forward–backward stochastic differential equations (FBSDEs in short) and an equilibrium condition. Then by decoupling the flow of FSBDEs, an explicit representation of an equilibrium solution is derived as well as its corresponding objective function value.     

Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks

A catastrophe may affect different locations and produce losses that are rare and highly correlated in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimentional distribution of claims from different locations depends on decision variables such as the insurer's coverage at different locations, on spatial and temporal characteristics of possible catastrophes and the vulnerability of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfolios to catastrophic risks requires geographically explicit simulations of catastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of what-if evaluations. The aim of this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on coverages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments.     

Non-zero-sum stochastic differential reinsurance and investment games with default risk

This paper investigates the implications of strategic interaction (i.e., competition) between two CARA insurers on their reinsurance-investment policies. The two insurers are concerned about their terminal wealth and the relative performance measured by the difference in their terminal wealth. The problem of finding optimal policies for both insurers is modelled as a non-zero-sum stochastic differential game. The reinsurance premium is calculated using the variance premium principle and the insurers can invest in a risk-free asset, a risky asset with Heston’s stochastic volatility and a defaultable corporate bond. We derive the Nash equilibrium reinsurance policy and investment policy explicitly for the game and prove the corresponding verification theorem. The equilibrium strategy indicates that the best response of each insurer to the competition is to mimic the strategy of its opponent. Consequently, either the reinsurance strategy or the investment strategy of an insurer with the relative performance concern is riskier than that without the concern. Numerical examples are provided to demonstrate the findings of this study.     

Equilibrium relationships between insurance and self-protection activity

When an insured understakes some costly self-protection activity that reduces the probability of loss, a competitive insurer will increase the insurance coverage, given a fixed premium per dollar of coverage, to reflect the lower insurance risk.However, an imperfectly informed insurer cannot correctly adjust the coverage; while he can observe the self-protection activity of the insured, the insurer cannot determine the cost to the insured of such activity, nor can the insurer determine the reduction in the loss probability of the insured due to the self-protection activity.This paper demonstrates in an equilibrium model that insurers may be able to use the amount of self-protection activity by an insured as a screen to indicate to the insurer what the loss probability of the insured is, thus allowing the insurer to provide correctly priced insurance to all individuals. The model points out that insurers operating in a market with moral hazard may be able to overcome the adverse incentives of insureds by selectively offering certain insurance contracts contingent upon the insured meeting certain screening requirements; in the model here, self-protection activity is the screen.     

Robust non-zero-sum investment and reinsurance game with default risk

This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, who are concerned about the potential model ambiguity and aim to seek the robust optimal reinsurance and investment strategies. The ambiguity-averse insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks; and can invest in a financial market consisting of one risk-free asset, one risky asset and one defaultable corporate bond. The objective of each insurer is to maximize the expected exponential utility of his terminal surplus relative to that of his competitor under the worst-case scenario of the alternative measures. Applying the techniques of stochastic dynamic programming, we derive the robust Nash equilibrium reinsurance and investment policies explicitly and present the corresponding verification theorem. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium reinsurance and investment strategies and draw some economic interpretations from these results.     

Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

传统的保险市场难以满足日益频发的巨灾风险分散需求,巨灾债券作为一种非传统金融创新工具提供了一种新的分散机制,而精准定价则对巨灾债券的成功发行与交易起着关键作用。本文基于风险中性测度技术,在Longstaff随机利率且巨灾风险累积损失服从复合泊松损失条件下,得到了零息票巨灾债券价格公式;进一步结合广东省1989~2015年台风风暴潮灾害损失数据进行实证分析;最后,针对定价公式复杂性,本文利用快速傅里叶变换方法进行数值求解,结果验证了本文所构模型的可行性。本文的研究是希望能为我国发行巨灾债券与风险测度提供一定的理论基础与技术支持。     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

论保险投资新政对寿险公司投资收益的影响

近年来,保险监管部门颁布了多项保险投资新政,保险资金运用上的限制得到了放松.保险投资新政的实施对寿险公司投资收益有着怎样的影响呢?运用双重差分模型(DID模型),定量估计了保险投资新政实施前后的寿险公司投资收益的具体变化,并分析了何种因素对寿险公司的投资收益有显著影响.研究发现,保险投资新政对寿险公司的总投资收益率的提高有着积极的影响,保险投资新政对不同规模的寿险公司投资收益的影响存在着差异,仅考虑政策的调整因素,大型寿险公司的总投资收益率增量超过中小型寿险公司1.13%,综合考虑其它指标的影响后,其总投资收益率增量仍然超过中小型寿险公司0.097%.实证结果为保险监管部门的政策实施以及寿险公司的经营提供了新思路.     

Term structure of discount rates for firms in the insurance industry

There is strong evidence in the literature for the hypothesis that interest rates and the market risk premium are not constant during the business cycle. The beta risk of firms in the insurance industry is also time-varying. The major implication of these results is that discount rates for risky cash flows are time varying and must obey a term structure similar to the term structure of interest rates. The purpose of this paper is to estimate discount rates for cash flows with different time horizons for the U.S. insurance industry and for different insurance sectors. We find that the term structure cost of capital takes on different shapes depending on the business cycle. It is therefore meaningful for insurers to evaluate risky projects by selecting a discount rate most appropriate for the nature and the time horizon of each project.     

Stochastic portfolio specific mortality and the quantification of mortality basis risk

In the last decade a vast literature on stochastic mortality models has been developed. However, these models are often not directly applicable to insurance portfolios because:

(a) For insurers and pension funds it is more relevant to model mortality rates measured in insured amounts instead of measured in the number of policies.

(b) Often there is not enough insurance portfolio specific mortality data available to fit such stochastic mortality models reliably.

Therefore, in this paper a stochastic model is proposed for portfolio specific mortality experience. Combining this stochastic process with a stochastic country population mortality process leads to stochastic portfolio specific mortality rates, measured in insured amounts. The proposed stochastic process is applied to two insurance portfolios, and the impact on the Value at Risk for longevity risk is quantified. Furthermore, the model can be used to quantify the basis risk that remains when hedging portfolio specific mortality risk with instruments of which the payoff depends on population mortality rates.     

Asset and liability modelling for participating policies with guarantees

We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the dynamic equations. Thus large-scale problems are solved with standard methods. We report on an empirical analysis of policies offered by Italian insurers. The optimized model results are in general agreement with current industry practices. However, some inefficiencies are identified and potential improvements are highlighted.     

Global loss diversification in the insurance sector

We study the possibility for international diversification of catastrophe risk by the insurance sector. Adopting the argument that large insurance losses may be a ‘globalizing factor’ for the industry, we study the dependence of geographically distant insurance markets via equity returns. In particular, we employ conditional copula theory to model the bivariate dependence of the insurance industry. In contrast to earlier literature on this subject, we disentangle the causes of dependence stemming from the asset side from those from the liability side by conditioning on general market conditions. We find that for both Europe-America and Europe-Asia the dependence is significant. Moreover, we find asymmetric effects: the international dependence is particularly high for losses, even after conditioning for the asset side dependence. Finally, we investigate the time variation in copula parameters and find evidence that dependence in the insurance sector has increased over time, thus reducing the scope for international diversification of large losses in this sector.     

The Hungarian insurance market structure: an empirical analysis

This paper analyzes the market structure of the Hungarian insurance market, which operated as a monopoly market until 1986. After the regime change this sector started to develop rapidly. But the Hungarian insurance market has a strong oligopolistic character, and thus raises an interesting question as to how close the market is to a state of perfect competition. Based on the Panzar and Rosse (J Ind Econ 35:443–456, 1987) methodology we estimate the elasticity of total revenues with respect to changes in input prices, so that we can determine the market structure. The estimation of input price elasticity is made with a static and a dynamic panel model. According to research the structure of the Hungarian insurance market significantly differs from the perfect competition case between 2010 and 2019. The market is in long-run equilibrium, and the hypothesis of the monopoly case cannot be rejected. The market structure of a sector is important for modelling phenomena and new regulations effectively, which is relevant for insurance and competition supervision in the protection of customers.

     

An optimal co-reinsurance strategy

This article considers a co-reinsurance strategy that (1) protects insurance companies against catastrophic risks; (2) enables insurers to gather sufficient information about the different risk attitudes of reinsurers and diversify their reinsured risks; (3) enables insurers to create better risk-sharing profiles by balancing the risk tolerances of reinsurers; (4) has the benefit of allowing reinsurers to accumulate experience with risks with which they are unfamiliar; (5) reduces the overall direct cost of a reinsurance contract; (6) allows a government to back some insurance products, such as the terrorism insurance programs that were established in many countries after the September 11th terrorist attacks; and (7) reflects the practical reinsurance industry of some countries, such as Iran. Such a co-reinsurance strategy can be fully determined by estimating its parameters whenever three optimal criteria are satisfied and prior information about the unknown parameters is available. Two simulation-based studies have been conducted to demonstrate (1) the practical applications of our findings and (2) the possible impact of any type of dependency between the co-reinsurance’s parameters and the evaluated optimal co-reinsurance strategy.     

Organization and efficiency in the international insurance industry: A cross-frontier analysis

This paper employs cross-frontier analysis, an innovative tool based on data envelopment analysis, to provide new insight into the relationship between organization and efficiency in international insurance markets. We are the first to empirically test the expense preference hypothesis and the efficient structure hypothesis in a large cross-country study. For this purpose, we consider 23,807 firm-years for 21 countries from northern America and the European Union—a dataset not previously analyzed in this context. We find evidence for the efficient structure hypothesis in selected market segments, but we find no evidence for the expense preference hypothesis. Our results provide insight into the competitiveness of stock and mutual insurers from different countries. At the country level, the results can be used to compare different insurance markets. Our findings are especially interesting for the strategic management of insurance companies as well as for regulators and boards of national insurance associations.