Interplay of insurance and financial risks in a stochastic environment

Consider an insurer who makes risky investments and hence faces both insurance and financial risks. The insurance business is described by a discrete-time risk model modulated by a stochastic environment that poses systemic and systematic impacts on both the insurance and financial markets. This paper endeavors to quantitatively understand the interplay of the two risks in causing ruin of the insurer. Under the bivariate regular variation framework, we obtain an asymptotic formula to describe the impacts on the insurer's solvency of the two risks and of the stochastic environment.     

Parameter risk in time-series mortality forecasts

The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland.     

QIS4 – Konzeption des europäischen Standardansatzes und Kapitalausstattung für Schaden-Unfallversicherer – Analyse und Beurteilung

The paper examines the updated requirements for risk based capital evaluation within the framework of the European Solvency??II project. The early results for the quantitative impact study QIS4 will be shown and feasible effects on the insurance industry will be derived. In contrast to the previous system, Solvency??II is based on a market value approach which gives incentives to insurance companies to improve their internal risk management and assessment procedures through the enforcement of riskadequate illustration of the overall risk position. Here probability distributions are calculated for each risk categories in the standard approach. For this reason a quantitative term is derived to assess the overall risk position of an insurer which arises from the aggregation of each single risk considering the diversification effect. The extent of uncertainty is predetermined by the legislator. For the acceptance of future arrangements it will be important to answer the question whether these approaches are manageable and adequate.     

Financial Intermediary Versus Production Approach to Efficiency of Marketing Distribution Systems and Organizational Structure of Insurance Companies

An examination of the efficiency of the marketing distribution channel and organizational structure for insurance companies is presented from a framework that views the insurer as a financial intermediary rather than as a “production entity” which produces “value added” through loss payments. Within this financial intermediary approach, solvency can be a primary concern for regulators of insurance companies, claims‐paying ability can be a primary concern for policyholders, and return on investment can be a primary concern for investors. These three variables (solvency, financial return, and claims‐paying ability) are considered as outputs of the insurance firm. The financial intermediary approach acknowledges that interests potentially conflict, and the strategic decision makers for the firm must balance one concern versus another when managing the insurance company. Accordingly, we investigate the efficiency of insurance companies using data envelopment analysis (DEA) having as insurer output an appropriately selected (for the firm under investigation) combination of solvency, claims‐paying ability, and return on investment as outputs. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination. Comparisons with the “value‐added” or “production” approach to insurer efficiency are presented. A new DEA approach and interpretation is also presented.     

Topical modelling issues in Solvency II

The main reasons for giving European insurance companies the option to apply internal models for calculating the main solvency requirement within the Solvency II framework is to enhance better risk management in the firms, and to provide the opportunity to derive a more accurate risk-oriented capital requirement than the standard Solvency Capital Requirement (SCR) could provide. The possibility to use internal models within pillar 1 basically means freedom to calculate the solvency requirement using some other formula and even principles than those given by the standard formula. This freedom is more limited with partial models.

This paper gives a brief introduction and update to the Solvency II project, reviews and discusses some topical aspects of internal models from the supervisory point of view, and points out some relating results of the Quantitative Impact Studies carried out, thus far, in the EU by CEIOPS.     

保险公司偿付能力风险信息对称性与市场供求

保险公司偿付能力充足性是保险监管的内容之一,但是这一信息却往往不被投保人所获知,造成保险供给(保险公司)和保险需求(投保人)两方信息的不对称.本文以保险公司存在偿付能力风险为基本假定,以累积性预期理论和风险调整资本收益率构建保险需求和供给模型,分析在信息对称条件下和信息不对称条件下保险需求的变化及其对保险供给和保险公司...     

Competition,efficiency and soundness in European life insurance markets

This paper provides cross-country evidence on the association between soundness and competition in the life insurance industry, where competition is measured by the Boone indicator. We analyse 10 European Union (EU) life insurance markets over the post-deregulation period 1999–2011. The results indicate that competition increases the soundness of the EU life insurance markets. Since the Boone indicator measures competition based on the reallocation of profits from inefficient insurers to efficient ones, our results suggest that efficiency is the mechanism through which competition contributes to insurer solvency. The soundness-enhancing effect of competition is greater for weak insurers than for healthy ones.     

Capital and risk in property-liability insurance markets

This paper investigates the capital and portfolio risk decisions of property-liability insurance firms. A theoretical model based on option pricing theory is developed which predicts a positive relationship between insurer capital and risk, as firms balance these two factors to achieve their desired overall insolvency risk. The implications of the model are then tested empirically using a simultaneous equations methodology. The results support the predictions of the model. They also provide evidence that managerial incentives play a role in determining capital and risk in insurance markets. The findings have significant implications for insurance solvency regulation.     

Biometric Solvency Risk for Portfolios of General Life Contracts. I. The Single-Life Multiple Decrement Case

Abstract

Solvency II splits life insurance risk into seven risk classes consisting of three biometric risks (mortality risk, longevity risk, and disability/morbidity risk) and four nonbiometric risks (lapse risk, expense risk, revision risk, and catastrophe risk). The best estimate liabilities for the biometric risks are valued with biometric life tables (mortality and disability tables), while those of the nonbiometric risks require alternative valuation methods. The present study is restricted to biometric risks encountered in traditional single-life insurance contracts with multiple causes of decrement. Based on the results of quantitative impact studies, process risk was deemed to be not significant enough to warrant an explicit calculation. It was therefore assumed to be implicitly included in the systematic/parameter risk, resulting in a less complex standard formula. For the purpose of internal models and improved risk management, it appears important to capture separately or simultaneously all risk components of biometric risks. Besides its being of interest for its own sake, this leads to a better understanding of the standard approach and its application extent. Based on a total balance sheet approach we express the liability risk solvency capital of an insurance portfolio as value-at-risk and conditional value-at-risk of the prospective liability risk understood as random present value of future cash flows at a given time. The proposed approach is then applied to determine the biometric solvency capital for a portfolio of general life contracts. Using the conditional mean and variance of a portfolio’s prospective liability risk and a gamma distribution approximation we obtain simple solvency capital formulas as well as corresponding solvency capital ratios. To account for the possibility of systematic/parameter risk, we propose either to shift the biometric life tables or to apply a stochastic biometric model, which allows for random biometric rates. A numerical illustration for a cohort of immediate life annuities in arrears reveals the importance of process risk in the assessment of longevity risk solvency capital.     

Der Einsatz interner Modelle beim mehrj?hrigen Enterprise Risk Management

Increasing natural catastrophes, recent dynamics in capital markets, and fundamental changes in regulatory requirements (e.g., Solvency II for European Union member countries) have placed increasing challenges in management of insurance companies. While in the Solvency II framework the time horizon is one year, the strategic risk-return profile of the insurer should be set according to multi-year calculations. The aim of this paper is to introduce a multi-year risk-capital concept. This multi-year approach can help management to answer the following essential question: ??How many future years with extreme catastrophes or adverse capital market developments can the company withstand at a certain confidence level without external capital supply??? In the context of multi-year enterprise risk management a capital allocation method is needed in order (1) to set risk limitations for different segments, for example different lines of business and different years, and (2) to quantify the effect of management strategies on risk-adjusted performance indicators, defined per segment. We define a capital allocation method in the multi-year context and illustrate the use of the multi-year risk-capital concept within a simulation study.     

Optimal Insurance With Costly Internal Capital

We introduce costly internal capital into a standard insurance model, in which a risk‐averse policyholder buys insurance from a risk‐neutral insurer with limited liability. The unique optimal contract and internal capital lead to a strictly positive probability for insurer default. Some risks are uninsurable in that the insurer chooses not to provide insurance against such risks. An increase in the cost of capital may lead to a higher optimal amount of internal capital. The results extend to multiple policyholders in a symmetric setting. Our extension of the classical model to include costly internal capital provides a fruitful approach to many real world insurance markets.     

Solvency, Capital Allocation, and Fair Rate of Return in Insurance

In this article, we consider the links between solvency, capital allocation, and fair rate of return in insurance. A method to allocate capital in insurance to lines of business is developed based on an economic definition of solvency and the market value of the insurer balance sheet. Solvency, and its financial impact, is determined by the value of the insolvency exchange option. The allocation of capital is determined using a complete markets’ arbitrage‐free model and, as a result, has desirable properties, such as the allocated capital “adds up” and is consistent with the economic value of the balance sheet assets and liabilities. A single‐period discrete‐state model example is used to illustrate the results. The impact of adding lines of business is briefly considered.     

Überlegungen zu einem fairen Risikomanagement-Mix in Versicherungsunternehmen

This article deals with the question of how a ?fair risk management mix“ that does not lead to a wealth transfer between shareholders and policyholders can be achieved in a joint-stock insurance company. In our financial model of an insurer, the ?fair“ situation, it is assumed that there is no wealth transfer between shareholders and policyholders when both parties receive a net present value of zero on their investments. Taking the default risk of the insurance company into account, we first model a ?fair“ situation for the insurer’s existing portfolio. Surprisingly, closing a new insurance contract that has been priced on a fair basis and then included in the insurer’s existing portfolio leads to a disequilibrium situation because the net present value for the shareholders is no longer zero. This new net present value can be viewed as the fair price of any risk management measure the insurer must take so as to reestablish an equilibrium for both parties, the shareholders and the policyholders.     

国际保险业偿付能力监管制度比较及发展趋势研究

偿付能力监管是各国保险业监管的核心,此次金融危机揭示出原有的保险偿付能力监管制度存在巨大的缺陷。本文对美国、加拿大、百慕大、澳大利亚、英国、瑞士、欧盟等七个国家或地区的监管体制进行了比较研究,分析各国在风险的识别方式、风险评估模型及偿付能力监管报告和检查制度上的共性与特征,介绍可能的发展趋势,并为我国完善偿付能力监管制度提出了建议。     

Die Risikoübernahme von Versicherungsunternehmen: Eine empirische Analyse für Deutschland und Großbritannien

In this paper we analyze the risk resulting from an insurer’s investment policy. For this a hypothetical asset return rate is defined, based on which the German and British insurance market is analyzed. The study design allows an investigation of the investment risk in different countries or for different lines of business. The aim of the analysis is to detect general market trends in the investment policy and an analysis of effects of important changes over time on the investment risk of insurers. The questions analyzed in this paper are also of particular relevance beyond the background of current reform proposal for insurance regulation in Europe in the field of risk management and capital adequacy (Solvency II).     

Optimal insurance in the presence of reinsurance

This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution.     

我国保险公司偿付能力报告改进的探讨

保险公司偿付能力报告是保险监管部门基于监管的需要要求保险公司定期报送的报告,保险监管部门希望根据这套报告来判断保险公司现在偿付能力是否充足,并预测保险公司未来偿付能力的变化。我国的偿付能力报告制度正在逐渐建立,笔者认为我国现行的偿付能力报告的内容存在一些问题,需要改进。本文从分析偿付能力报告目标出发,对现有的偿付能力报告提出一些改进建议,包括:建立预警指标体系形成多指标评价标准;增加现金流量信息;改善风险管理制度披露的内容;完善动态偿付能力测试的规定。     

Lévy insurance risk process with Poissonian taxation

The idea of taxation in risk process was first introduced by Albrecher, H. & Hipp, C. Lundberg’s risk process with tax. Blätter der DGVFM 28(1), 13–28, who suggested that a certain proportion of the insurer’s income is paid immediately as tax whenever the surplus process is at its running maximum. In this paper, a spectrally negative Lévy insurance risk model under taxation is studied. Motivated by the concept of randomized observations proposed by Albrecher, H., Cheung, E.C.K. & Thonhauser, S. Randomized observation periods for the compound Poisson risk model: Dividends. ASTIN Bulletin 41(2), 645–672, we assume that the insurer’s surplus level is only observed at a sequence of Poisson arrival times, at which the event of ruin is checked and tax may be collected from the tax authority. In particular, if the observed (pre-tax) level exceeds the maximum of the previously observed (post-tax) values, then a fraction of the excess will be paid as tax. Analytic expressions for the Gerber–Shiu expected discounted penalty function and the expected discounted tax payments until ruin are derived. The Cramér-Lundberg asymptotic formula is shown to hold true for the Gerber–Shiu function, and it differs from the case without tax by a multiplicative constant. Delayed start of tax payments will be discussed as well. We also take a look at the case where solvency is monitored continuously (while tax is still paid at Poissonian time points), as many of the above results can be derived in a similar manner. Some numerical examples will be given at the end.     

Informations- und Beratungspflichten des Versicherers nach der VVG-Reform

The insurer’s duty to enable the customer to come to an appropriate decision, providing advice and information, is a central topic of the reform of the German insurance contract law. The obligations of intermediaries given by the Directive 2002/92/EC on insurance mediation are transferred to insurers and thereby enlarged in some aspects. The duty to give advice in §6 I 1 VVG depends on the objective circumstances of each individual case depending upon either the complexity of the insurance contract and problems in understanding its terms, or the characteristics and situation of the customer. Therewith, the regulation both refers to former jurisdiction and exceeds it by implementing a duty for the insurer to ask for the demands and the needs of the customer. Without reason in the special case the customer has to disclose his need for advice to obtain it. During the term of the contract the insurer is only obliged to give advice if he knows or — acting diligently — could know the needs of the policy-holder. On a European level further duties to inform and advise could help to achieve an effective internal insurance market.     

Die Gruppenaufsicht nach dem Entwurf der Solvency II Rahmenrichtlinie

The draft framework directive for Solvency II (“Draft”) in general and the section on group supervision in particular is an impressive step towards a modern supervisory system, which is aligned with the economical reality of the insurance groups. It is to be hoped that the Draft will be implemented with only few changes.The Draft distinguishes a general and a special (group support regime) group supervision. The general group supervision constitutes a much more modern concept than the current Insurance Groups Directive, since it partly modifies the solo supervision (internal model to be approved by the group supervisor) and introduces a group based solvency requirement, the calculation of which allows for diversification effects on a group level.The group support regime, which applies only if an application has been approved by the group supervisor, allows to recognise such diversification effects by allowing the parent undertaking to replace paid-up own funds in a subsidiary undertaking by a group support declaration. Conditions for group support are in particular that the respective subsidiary is subject to an integrated risk management and internal control system, that the group solvency requirement is covered with own funds, and that the parent undertaking commits to promptly transfer own funds to the subsidiary where necessary, up to the limit of the group support declaration.