Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Converting retirement benefit into a life care annuity with graded benefits*

This paper deals with life care annuities, i.e. bundled products comprising a life annuity and long-term care insurance. It aims to assess the cost of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. With this objective in mind, we present an actuarial method based on array calculus for valuing this type of life care annuity. The health dynamics of the annuitant rely on a reversible illness-death multistate framework. The paper contains a numerical example in which mortality and disability assumptions are based on data from the USA and Australia, although this should be viewed simply as an illustration. In addition, in order to check the coherence of these data, we compute life expectancy for both healthy and dependent persons, and then for dependent persons in each of the states of dependence. The effect of ruling out the recovery assumption on the annuity’s cost is also assessed. The analysis provides valuable insights into how much it would cost to introduce these annuities and enables us to make some policy recommendations to help ensure that this combined pension scheme has a good actuarial design.     

The role of life insurance in an emerging economy: Human capital protection,assets allocation and social interaction

In this paper, we provide micro-econometric evidence on the determinants of life insurance demand in China, the largest emerging market in the world. We employ the China Household Income Project (CHIP) dataset for the year 2002 in the analysis. The timing is ideal, because of the nature of the less well developed capital markets and social security systems in China in 2002, which sets a suitable stage to study the insurance demand behavior of emerging markets. The results indicate that both the human capital protection motive and the asset allocation motive are important in explaining the purchase of life insurance in China. In addition, we present three empirical regularities: (1) the positive correlation between the returns to human capital and the returns to market portfolio decrease the demand for life insurance; (2) both the current wealth and future income of a household exert curvilinear impacts on life insurance demand; (3) the breadth of a households social connections has substantial impacts on life insurance demand.     

Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios

Many investors believe that they can effectively reduce risk by, among other ways, holding large combinations of investment assets. The purpose of this paper is to develop asymptotic approximations of the windfall and shortfall probabilities for an optimal portfolio of risky assets as the number of the assets becomes sufficiently large. We start by providing some heuristics to motivate our problem, then proceed to prove general large deviations theorems. We also present specific results with an application to the multivariate normal case. Both a theoretical analysis of the method and an empirical application justify the diversification tenet of the allocation strategies that many hedge funds and pension funds tend to adopt nowadays.     

Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios

This paper investigates the ordering properties of the largest claim amounts and sample ranges arising from two sets of heterogeneous portfolios. First, some sufficient conditions are provided in the sense of the usual stochastic ordering to compare the largest claim amounts from two sets of independent or interdependent claims. Second, comparison results on the largest claim amounts in the sense of the reversed hazard rate and hazard rate orderings are established for two batches of heterogeneous independent claims. Finally, we present sufficient conditions to stochastically compare sample ranges from two sets of heterogeneous claims by means of the usual stochastic ordering. Some numerical examples are also given to illustrate the theoretical findings. The results established here not only extend and generalize those known in the literature, but also provide insight that will be useful to lay down the annual premiums of policyholders.     

Ruin probabilities and aggregrate claims distributions for shot noise Cox processes

We consider a risk process R _t where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically adjusted according to past claims experience.     

Uncertainty on survival probabilities and solvency capital requirement: application to long-term care insurance

In this paper, we focus on uncertainty issues on disabled lives survival probabilities of LTC insurance policyholders and its consequences on solvency capital requirement. Among the risks affecting long-term care portfolios, special attention is addressed to the table risk, i.e. the risk of unanticipated aggregate mortality, arising from the uncertainty in modeling LTC claimants survival law. The table risk can be thought as the risk of systematic deviations referring not only to a parameter risk but, as well, to any other sources leading to a misinterpretation of the life table resulting for example from an evolution of medical techniques or a change in rules of acceptance. In fine, the idea is to introduce the risk of systematic deviations arising from the uncertainty on the disabled lives death probabilities directly. We analyze the consequences of an error of appreciation on the disabled lives survival probabilities in terms of level of reserves and describe a framework in an Own Risk and Solvency Assessment perspective to measure the gap between the risk profile from the standard formula to the risk analysis specific to the organism.     

临时保险制度：赔付理由、期间及其限制

我国《保险法》未规定临时保险制度,本文建议,我国的临时保险制度应当分为强制临时保险与自愿临时保险两种,在保险人预收保险费的情况下,根据履行提前、对价平衡、合理期待等理论,保险人应当对临时保险事故予以赔付,此种临时保险的期间自投保人交付保险费之时起算,于正式保险生效之时或投保人收到拒保通知书并由保险人退还保险费之时终止;...     

Mortgages and bonds: The asset management practices of Australian life insurers to 1960

Recent studies of the experience of the British life insurance industry indicate that a period of transition, and the development of more diversified investment strategies, began in the interwar period. Australian life insurers lagged behind their British counterparts in the introduction of such strategies. This paper investigates why this was the case. It argues that in the Australian market there was both a lack of opportunity and incentive to broaden asset portfolios. However, this did not mean that asset management practices did not advance. Australian life offices became progressively more sophisticated in their approach to portfolio management during this period. Developments in the interwar period provided a grounding for post-war expansion into the equity market.     

保险"理赔难"的原因及解决对策

探讨保险“理赔难”的原因所在,并从保监会、投保人和保险人以及行业发展方向等各方面入手,思考如何解决保险“理赔难”的问题。     

中国财产保险业巨灾损失赔付能力实证研究

中国社会已步入一个历史性的风险高度累积的发展阶段,在这样的环境中,以损失补偿为主要功能的财产保险业是否有足够的损失赔付能力就成为一个不能不考虑的重要问题。本文基于Cummins,Doherty和Anita(2002)的保险赔付能力度量模型,引入1998年～2007年中国保险业经营数据,在改进后的损失对数正态分布假设下,对2007年年末时点上在中国大陆经营财产保险业务的39家保险公司以及全行业整体巨灾损失赔付能力进行了实证分析。结果显示,在800亿到2000亿元的巨灾损失区间内,中国财产保险业的赔付效率在68.36%以上,全行业巨灾赔付能力缺口巨大,且损失幅度越大短缺的幅度越大。本文认为,造成这种赔付能力短缺的主要原因在于全行业资本与盈余的低水平以及再保险市场发展的严重滞后。     

Risk-based capital for credit insurers with business cycles and dynamic leverage

This paper develops a risk-based capital pricing model for credit insurance portfolios held by a vulnerable insurer. The model accounts for business cycles using a two-state Markov switching model, and allows for dynamic leverage adjustment by the insured firms. The new proposed model, which incorporates risk-based capital practice, is better for both the insurer and the insured firms. Based on the risk-adjusted performance metric, we found that the insurer is better off insuring short- and medium-term loans in expansion and steady states, while it is better off backing both short- and long-term loans in recessions. Our results also emphasize that macroeconomic uncertainty significantly impairs the creditworthiness of the insurer and insured firms.     

Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks

This contribution focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account and they are equipped with a wide type of dependence structure. We derive precise asymptotic formulas for the ruin probabilities when the insurance risk has a dominatedly varying tail. In the special case of regular variation, the corresponding formula is proved to be uniform for the time horizon.     

A novel equity valuation and capital allocation model for use by long-term value-investors

We present a novel asset pricing model that captures the investment wisdom and stock-selection approach of the long-term value-investors Benjamin Graham and Warren Buffett. Taking a longer term view of business prospects and business risks, we explicitly consider the time period in which a business enjoys a competitive advantage over its peers as the central tenet of our model and capture the eventual demise of this competitive advantage in a probabilistic manner. Assuming that our investor has log utility, our model answers the question of capital allocation in a two-asset scenario. The model does not enforce the Efficient Market Hypothesis and is shown to explain some well-known empirical studies on stock returns.     

Optimal asset allocation for participating contracts under the VaR and PI constraint

ABSTRACT

Participating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth.     

Costly information production and optimal capital structuring: Theory and implications for finance and accounting

By considering a broad class of securities offerings that we termcapital structurings, a firm can always avoid pooling with firms whose prospects are poorer. This result implies that firms need not indulge in costly information gathering, hoping thereafter to signal to investors. One application allows us to describe a new theory of capital structurings, in which firms choose their capital structure not (as in traditional capital structure signaling theory) to signal privately known prospects, but rather to signal that no (productively useless) investigation of prospects has been pursued. A second application addresses the issue of the impossibility of informationally efficient capital markets: firms are capable of establishing conditions under which investors will recognize informational efficiency. The authors wish to acknowledge helpful comments by participants in seminars at the University of Hawaii at Manoa and the Univeristy of Tsukuba. Particular thanks go to Adam Brandenburger and an anonymous referee. Naturally, any remaining errors are the responsiblity of the authors. C.J.J. is on leave at the Council of Economic Advisers. This article reflects the opinions of the authors and not that of the Council of Economic Advisers. Much of the work for this article was conducted while E.H.R. was on leave at the Institute of Socio-Economic Planning at the University of Tsukuba, Tsukuba, Ibaraki 305, Japan.     

家庭人口结构与家庭商业人身保险需求——基于中国家庭金融调查(CHFS)数据的实证研究

本文使用2013年中国家庭金融调查(CHFS)数据,从微观层面探讨家庭人口结构对家庭人身保险需求的影响。Probit和Tobit实证结果显示,家庭老年人口占比与家庭人身保险需求负相关,这意味着,人口老龄化对人身保险产品的需求会起到抑制作用。家庭少儿人口占比与家庭人身保险需求则呈正相关,这显示少儿人口的增加会推动人身保险市场的发展。家庭就业者占比对家庭人身保险需求有抑制作用。同时,缩小的家庭规模有助于增加对人身保险产品的需求。我们的研究对深刻理解当下中国面临的人口老龄化问题及计划生育政策有一定的参考价值。     

政策性农业保险补贴的最优边界与方式探讨

政策性农业保险补贴具有动态性和多维性的最优边界,补贴的不足和过高均会减少福利。本文将消费者剩余和外部性结合起来构建了农业保险的福利经济学模型,探讨了最优补贴边界的决定标准;从保户和保险机构两方面分析了直接补贴原保险相对低效率的原因所在,提出了涵盖运作主体、基金运作方式、费率和再保险责任限制方式等要素的以再保险补贴为核心的最优补贴方式的构想。相对于直接补贴原保险的做法,这种构想更有利于实现农业风险的分散,减少信息不对称,提高转移支付的效率,进而实现农业保险供给的扩张。     

保险公司资产组合与最优投资比例研究

保险公司收益主要来源于承保利润和投资收益,其中承保利润受政策变动、市场条件等外部环境的影响较大,而投资收益则更多地取决于保险公司的投资能力,因此保险公司如何构建资产组合、如何确定最优投资比例就是获取投资收益最大化的重要因素。本文通过理论推导得出了保险公司的资产组合模型并运用非线性规划求解出最优投资比例,进而根据保险公司的投资数据进行了实证研究,为我国保险公司的资产组合及最优投资比例提供了一个可借鉴的思路。