Exotic unit-linked life insurance contracts

This article integrates aspects of traditional insurance with advances in financial economics, yielding proper valuation and premium assessments of insurance benefits linked to various financial assets. Several new types of unit-linked life insurance contracts are discussed, with substantial potential for real-life applications. Compared to usual unit-linked products, these contracts offer added flexibility and/or altered exposure to financial risk for the insured and/or the insurer. The single premiums of these policies are calculated as expectations under a risk-adjusted probability measure (equivalent martingale measure), satisfying no-arbitrage conditions in financial markets.     

About a duration index for life insurance contracts

Abstract

In this paper, after having defined the duration for a “generic” life insurance contract, we bring out some of its properties. We also prove that, in some cases, duration is a natural extension of well-known duration indices.     

The pricing of equity-linked life insurance policies with an asset value guarantee

This paper considers the equilibrium pricing of equity-linked life insurance policies with an asset value guarantee; such policies provide for benefits which depend upon the performance of a reference portfolio subject to a minimum guaranteed benefit. The benefit is decomposed into a sure amount and an immediately exercisable call option on the reference portfolio. A numerical procedure for determining the value of the call option is presented and the risk minimizing investment strategy to be followed by the issuer of the policy is derived.     

Regression-based algorithms for life insurance contracts with surrender guarantees

We present a general framework for pricing life insurance contracts embedding a surrender option. The model allows for several sources of risk, such as uncertainty in mortality, interest rates and other financial factors. We describe and compare two numerical schemes based on the Least Squares Monte Carlo method, emphasizing underlying modeling assumptions and computational issues.     

A performance analysis of participating life insurance contracts

Traditional life insurance products, in particular participating life insurance contracts, are often criticized. Their performance is often said to be poor compared to other investment alternatives. Interestingly, this perception appears to persist although very little research has been conducted into the performance of participating life insurance contracts. But are participating life insurance contracts actually bad for policyholders? We conduct a performance analysis based on contracts offered in the German market, in order to provide evidence to support decision making by policyholders.     

On accounting standards and fair valuation of life insurance and pension liabilities

The actuarial profession is increasingly teaming up with financial economists for a fruitful cooperation on the proper valuation of life insurance and pension (L&P) liabilities. This has been a natural consequence of a recent sharply increased focus on market values in financial reports of L&P companies from regulators, standard setters, the financial press, stakeholders, and others with an interest in the L&P business.

This article provides a financial economist's point of view on recent developments in relation to the fair valuation of L&P liabilities. The role of accounting standards and the background for the international harmonization in this field are first discussed. We then review and explain the concept of fair value and provide a general view on appropriate techniques for estimating fair values of L&P liabilities in accordance with the definition of the concept. The paper also contains a section which briefly reviews recent and quite innovative regulatory initiatives in relation to market value reporting in the Danish market for life and pension insurance.     

寿险合同复效之立法变动及规范方向

保险合同的中止和复效是因人寿保险合同的保险费交付债务的特殊性而在保险法上的特别规定。其规定在强行性上属于半强性规范,是为保护危险团体成员的利益而设,保险人不能通过格式条款或其他方式予以排除适用,或作出较该规范更不利于危险团体成员利益的规定。为此,需要在立法上增加关于认知和判断半强性规范的效力性规定,同时,也需明确复效的具体条件,以消除保险人在实际上通过协商同意来操控处于效力停止状态的保险合同的命运,使危险团体成员的利益得以落实。     

Hierarchical structures in the aggregation of premium risk for insurance underwriting

In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group.

Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the independence case, generally the use of copula functions can consent to have the multivariate distribution under dependence assumptions too.

However, the choice of the copula and the parameter estimation could be very problematic when only few data are available. So it could be useful to find a closed formula based on Internal Models independence results with the aim to obtain the capital requirement under dependence assumption.

A simple technique, to measure the diversification effect in capital requirement assessment, is the formula, proposed by Solvency II quantitative impact studies, focused on the aggregation of capital charges, the latter equal to percentile minus average of total claims amount distribution of single line of business (LoB), using a linear correlation matrix.

On the other hand, this formula produces the correct result only for a restricted class of distributions, while it may underestimate the diversification effect.

In this paper we present an alternative method, based on the idea to adjust that formula with proper calibration factors (proposed by Sandström (2007)) and appropriately extended with the aim to consider very skewed distribution too.

In the last part considering different non-life multi-line insurers, we compare the capital requirements obtained, for only premium risk, applying the aggregation formula to the results derived by elliptical copulas and hierarchical Archimedean copulas.     

财产保险费率市场化的生成机制研究

我国财产保险费率市场化经历了管制——解除管制——管制三个阶段,目前,费率市场化的生成机制仍未形成。本文从财产保险定价的特殊性出发,探讨财产保险费率市场化应具备的特殊条件,以及促使上述条件得以生成的机制,并对费率市场化的两种生成机制进行比较分析,提出我国下一步费率政策改革的建议。     

Combining fair pricing and capital requirements for non-life insurance companies

The aim of this article is to identify fair equity-premium combinations for non-life insurers that satisfy solvency capital requirements imposed by regulatory authorities. In particular, we compare target capital derived using the value at risk concept as planned for Solvency II in the European Union with the tail value at risk concept as required by the Swiss Solvency Test. The model framework uses Merton’s jump-diffusion process for the market value of liabilities and a geometric Brownian motion for the asset process; fair valuation is conducted using option pricing theory. We show that even if regulatory requirements are satisfied under different risk measures and parameterizations, the associated costs of insolvency – measured with the insurer’s default put option value – can differ substantially.     

法院审理保险合同案件的两种解释方法比较

目前保险合同诉讼案件日趋增多,为探究当事人订立合同时的真正意图,不少法院采用了语境解释,当事人为证实自己的主张不断地举证,法院慎重地审查当事人提出的证据,但法院仍然存在错判的风险,而当事人诉讼成本的增加则是确定的。有时法院采用文本解释,即仅根据保险合同本身也能正确地判案,但诉讼成本大大降低。本文比较了这两种解释方法对法院判决保险合同案件准确性以及当事人花费诉讼成本的影响,指出文本解释优于语境解释。     

Optimal insurance contracts when establishing the amount of losses is costly

The problem of establishing the amount of losses covered by public and private insurance is often characterized by asymmetric information, in which the claimant already knows the extent of a loss but this can be demonstrated to the insurer only at a cost. It is shown that a simple arrangement, which provides greater coverage whenever individuals demonstrate high losses, gives claimants an excessive incentive to establish the amount of their losses. This paper determines what insurance claims process, consistent with the form typically employed in existing insurance arrangements, is optimal.     

The benefit of life insurance contracts with capped index participation when stock prices are subject to jump risk

We analyze the benefit to the insured of newly traded, innovative life insurance contracts. On a sequence of yearly reference days, the insured can choose between a guaranteed return (linked to the insurer’s asset result) and a capped index participation. The cap is adjusted at the beginning of each year such that both alternatives have the same value and the option to select is costless (product structuring condition). We point out that this condition cannot always be met. If the guaranteed return exceeds the upper bound of the capped index participation, the insurer can make a side profit. We show that a rather low insurance result also implies a rather low stock exposure, even if the insured opts for the index participation. Concerning the impact of the index dynamics, we emphasize that it is important to distinguish between jump and diffusion risk because the pricing of jump risk has an impact on cap rates that can be offered to an insured. Finally, we show that the optimal decision strategy of a CRRA investor implies an index selection even if it is unfairly priced such that the insurer indeed makes a side profit.     

Optimal insurance contracts without the non-negativity constraint on indemnities: revisited

In the literature on optimal indemnity schedules, indemnities are usually restricted to be non-negative. Keeler [1974] and Gollier [1987] show that this constraint might well bind: insured could get higher expected utility if insurance contracts would allow payments from the insured to the insurer at some losses. This paper extends Collier’s findings by allowing for negative indemnity payments for a broader class of insurers’ cost functions and argues that the indemnity schedule derived here is more appropriate for practical applications (e.g. in health insurance). JEL Classification D80 · D81 · D89     

中央财政森林保险保费补贴六省试点调研报告

为加快森林保险的发展,根据党中央、国务院有关文件精神,中央财政自2009年7月1日起在福建、江西和湖南三省启动了森林保险保费补贴试点工作,2010年7月1日起试点省又增加了浙江、辽宁和云南三省。我们通过书面调研、实地座谈、深入访谈等方式对试点六省的试点工作进展情况进行了较为广泛和深入的调查研究。同时,对11省的林业部门和人保财险17个省公司开展了问卷调查,并对问卷调查结果进行了统计分析。通过调查研究,总结了中央财政森林保险保费补贴政策试点以来取得的成效和存在的问题,分析了造成问题的原因,并在此基础上提出了政策建议。     

Utilizing NT-proBNP in the selection of risks for life insurance

Brain natriuretic peptide (BNP) is a counter-regulatory hormone produced mainly by ventricular myocardium. Early research studies were performed to ascertain its value in the diagnosis of congestive heart failure in acute care settings. Subsequent studies have explored its utility in screening for asymptomatic left ventricular dysfunction in the community, determining prognosis in coronary artery disease, appropriate timing of surgery in valve disorders, and in evaluating many other cardiac diseases. This review summarizes the current status of medical literature, introduces a new test to the insurance industry.     

我国保险格式条款行政监管比较分析

保险合同行政监管是各种保险合同监管方式中最早的一种,同时也是必不可少的一种。我国历来重视对保险格式条款的行政监管。《合同法》、2009年修订的《保险法》、《消费者权益保护法》以及不少地方性法规都不同程度地规定了保险合同监管的主体、内容、方式、原则、宗旨等,这些规定一方面整体确立了保险监管的基本框架,同时又划分了监管主体各自的监管疆界。     

论人身保险单的质押

人身保险单质押是权利质押.目前实践中主要以人身保险单的现金价值权为出质标的,从法律和质权的安全性考量,法律上应当明确人身保险单所表彰的投保人的现金价值权和被保险人、受益人的受益权均可以出质,投保人、被保险人、受益人均可作为出质人,而有关风险由质权人来考量和控制.人身保险单质权的设立和公示为确保交易便捷和安全,应当以登记...     

Simultaneous borrowing of information across space and time for pricing insurance contracts: An application to rating crop insurance policies

Changing climate and technology can often lead to nonstationary losses across both time and space for a variety of insurance lines including property, catastrophe, health, and life. As a result, naive estimation of premium rates using past losses will tend to be biased. We present three successively flexible data‐driven methodologies to nonparametrically smooth across both space and time simultaneously, thereby appropriately incorporating possibly nonidentically distributed data into the rating process. We apply these methodologies in estimating U.S. crop insurance premium rates. Crop insurance, with global premiums totaling $4.1 trillion in 2018, is an interesting application as losses exhibit both temporal and spatial nonstationarity. We find significant borrowing of information across both time and space. We also find all three methodologies improve both the stability and accuracy of crop insurance premium rates. The proposed methods may be of relevance for other lines of insurance characterized by spatial and/or temporal nonstationary losses.