To Sustain a Vital and Vibrant Actuarial Profession

Abstract

Insurance markets are different from most other markets. Insurance markets have an inherent self-destructive tendency that can cause market failure. However, insurance markets not only exist, they thrive. This paper explores the essential role that actuaries play in countering problems that can cause market failure. Armed with our mathematical and business skills and strong sense of professionalism, actuaries are essential to the successful growth of insurance companies and insurance markets. The breakdown of barriers among segments of the financial services industry creates an opportunity for actuaries to apply these same skills to noninsurance financial institutions. Actuaries have a strong claim to becoming the profession the public relies upon to ensure that an adequate balance is kept between profits and solvency. The foundation of this claim is not the superiority of our intellectual tools. It is the advantages to society of actuaries as a well-defined, recognized group of trustworthy and professional financial managers.     

“Statistical Independence and Fractional Age Assumptions”, Gordon E. Willmot,January 1997

Abstract

The People’s Republic of China has experienced substantial growth in insurance demand over the last decade. However, development of the related laws and regulations has not kept pace with the development of the insurance industry there. This paper reports on a pioneering study comparing different statutory reserve, solvency, and early warning systems in a sample of countries and regions in three of the world’s important economic regions–Asia, North America, and Europe. It begins with the construction of a model office applicable to the People’s Republic of China’s regulatory framework and unique market environment. Reserve standards and solvency measurement systems in different supervisory frameworks then are applied to the model office. The results are analyzed as a comparative study of the People’s Republic of China’s total assets required for the reserves and solvency margins under the practices of other jurisdictions. Early warning systems also are discussed.     

Insurance Guaranty Schemes in a Contingent Claims Setting

The introduction of an insurance guaranty scheme can have significant influence on the pricing and capital structures in a competitive market. This contribution summarizes the major findings of a working paper written by Schmeiser and Wagner (Working Papers on Risk Management and Insurance (IVW-HSG), No. 80, 2010). The effect on competitive equity-premium combinations is studied while considering a framework with policyholders and equity holders where guaranty fund charges are volume-based, as levied in existing schemes. Several settings with regard to the origin of the fund contributions are assessed and the immediate effects on the incentives of the policyholders and equity holders are analyzed through a one-period contingent claim approach. One result is that introducing a guaranty scheme in a market with competitive conditions entails a shift of equity capital towards minimum solvency requirements. Hence adverse incentives may arise with regard to the overall security level of the industry.     

Economic Capital Allocation Derived from Risk Measures

Abstract

We examine properties of risk measures that can be considered to be in line with some “best practice” rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk measure. As a consequence, conditions arise for comparison as well as for addition of risk measures. We demonstrate that imposing properties that are generally valid for risk measures, in all possible dependency structures, based on the difference of the risk and the solvency margin, though providing opportunities to derive nice mathematical results, violates best practice rules. We show that so-called coherent risk measures lead to problems. In particular we consider an exponential risk measure related to a discrete ruin model, depending on the initial surplus, the desired ruin probability, and the risk distribution.     

A Risk Model with Multilayer Dividend Strategy

Abstract

In recent years various dividend payment strategies for the classical collective risk model have been studied in great detail. In this paper we consider both the dividend payment intensity and the premium intensity to be step functions depending on the current surplus level. Algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu discounted penalty function and the expected discounted dividend payments are derived. This enables the analytical investigation of dividend payment strategies that, in addition to having a sufficiently large expected value of discounted dividend payments, also take the solvency of the portfolio into account. Since the number of layers is arbitrary, it also can be viewed as an approximation to a continuous surplus-dependent dividend payment strategy. A recursive approach with respect to the number of layers is developed that to a certain extent allows one to improve upon computational disadvantages of related calculation techniques that have been proposed for specific cases of this model in the literature. The tractability of the approach is illustrated numerically for a risk model with four layers and an exponential claim size distribution.     

Securitization and financial solvency: empirical evidence from Portugal

This paper analyses the effect of securitization issues on the solvency of Portuguese financial institutions. For this purpose, we use an unbalanced panel model estimated using GMM methods and find that securitization has a slightly positive impact on the soundness of the issuing entity. We study 35 financial entities and 60 traditional securitizations issued by 9 originators between 2001 and 2013. The analysis reveals that the financial entities’ soundness improved slightly, showing that securitization enhanced the quality of the originators’ portfolios and increased the regulatory capital requirements. We also found that efficiency and profitability improve the risk-adjusted ROAA and that efficiency increases regulatory capital requirements. The robustness analysis confirms the positive effect of securitization on solvency, where both credit quality and liquidity are shown to be significant variables.     

Bounds of ruin probabilities

Abstract

Upper and lower bounds are obtained for ruin probabilities with safety margin ρ in the case of known expectation, variance and range for the claim severity function.     

On the application of finance theory to the insurance firm

The primary argument set forth in this article is that the theory of finance can and should be rigorously applied to the study of the insurance firm. In order to illustrate this point, we turn our attention to the insurance solvency literature, where the implications of default risk for insurance company decision-making and regulatory policy are widely discussed but not nearly as widely understood. Rather than treat the probability of ruin as an exogenous constraint that is arbitrarily imposed by regulators, the approach taken here is to endogenize the probability of ruin with respect to a complex contracting process undertaken by a variety of self-interested claim holders. This treatment enables us to evaluate regulatory constraints such as minimum capital requirements within a rigorous theoretical framework. Our analysis suggests that even in an unregulated market, insurers would voluntarily limit their premium-capital ratios in an effort to economize on contracting costs. Furthermore, mutual insurers are likely,ceteris paribus, to employ less leverage than insurers organized as stock corporations.     

Aktienanlage für Lebensversicherer unter Solvency II

Life insurance companies are among the largest institutional investors. As part of their investment policy they are subject to special legal requirements. In particular the calculation of the solvency capital that has to be deposited for the market risk has changed under Solvency II. A widely spread thesis on this topic is that investments in equity have become unprofitable for life insurers due to solvency capital requirements – compared to previous periods of high equity ratios of temporally over 25%. Therefore insurers might have dropped their average stock quotas to below 5%.The intention of the present study is to analyze whether the capital requirements for the equity investments under Solvency II are a hurdle to achieve a reasonable profitability or – opposite to that – whether the equity investments are a suitable investment to provide an acceptable return on assets. For this purpose the solvency capital requirements of the equity investment under Solvency I considering the BaFin stress test are compared with the new solvency capital requirements under Solvency II including the symmetric adjustment factor (SA). Furthermore the diversification effects are taken into account; they are analyzed on the basis of the SFCR reports of the life insurance companies first published in 2017. As a result the risk capital requirements for equity investments under Solvency II have been reduced to more than 50% compared to prior solvency requirements and depending on the observed scenarios. Whilst Solvency I required an underlying risk capital of 31% at the end of 2017, Solvency II requires only 13.56% following the standard model and after aggregating the risk-mitigating effects in the group scenario. This effect results in a surplus of 7.2%, considering industry-standard capital costs for the underlying solvency capital and an average stock market return of 8% per annum. Consequently the equity investment is suitable to increase the profitability of the investments of German life insurance companies especially in the environment of low interest rates in the capital market for fixed income titles.     

Sharp approximations of ruin probabilities in the discrete time models

According to Solvency II directive, each insurance company could determine solvency capital requirements using its own, tailor made, internal model. This highlights the urgency of having fast numerical tools based on practically-oriented mathematical models. From the Solvency II perspective discrete time framework seems to be the most relevant one. In this paper, we propose a number of fast and accurate approximations of ruin probabilities involving some integral operator and examine them along strictly theoretical as well as numerical lines. For a few claim distributions the approximations are shown to be exact. In general, we prove that they converge with an exponential rate to the exact ruin probabilities without any restrictive assumptions on the claim distribution. A fast algorithm to approximate ruin probabilities by a numerical fixed point of the involved integral operator is given. As an application, ruin probabilities for, e.g. normally and Weibull – distributed claims are computed. Comparisons with discrete time counterparts of some continuous time approximation methods are also carried out. Numerical studies show that our approximations are precise both for small and large values of the initial surplus u. In contrast, the empirical De Vylder-type ones strongly depend on the claim distributions and are less precise for small and medium values of u.     

中国寿险业最低偿付能力额度要求研究

分析我国现行寿险业偿付能力额度标准理论,探讨现行标准的审慎性,并根据修正后的寿险业偿付能力额度的理论模型,采用中国寿险保险市场的历史数据进行了实证分析.     

The Impact of Introducing Insurance Guaranty Schemes on Pricing and Capital Structure

The introduction of an insurance guaranty scheme can have significant influence on the pricing and capital structures in a competitive market. The aim of this article is to study this effect on competitive equity–premium combinations while considering a framework with policyholders and equity holders where guaranty fund charges are volume‐based, as levied in existing schemes. Several settings with regard to the origin of the fund contributions are assessed and the immediate effects on the incentives of the policyholders and equity holders are analyzed through a one‐period contingent claim approach. One result is that introducing a guaranty scheme in a market with competitive conditions entails a shift of equity capital towards minimum solvency requirements. Hence, adverse incentives may arise with regard to the overall security level of the industry.     

An elusive panacea? The impact of the regulatory valuation regime on insurers' investment behaviour

This paper develops a framework to examine how the interactions between the valuation regime and solvency requirements influence investment behaviour of long-term investors with stable liabilities, such as life insurers. The results contribute to the debate over market-based valuation regimes, and shed light on new hybrid regimes explored in policy circles. We show that solvency requirements based on fair value regime can induce procyclical asset sales, but those based on historical cost valuation encourage insurers to engage in risk-shifting to the detriment of policyholders. A hybrid valuation regime, intended to address these unfavourable outcomes, does not strictly dominate the other two regimes on its own. However, market-based regimes can be made effective, if regulators calibrate their responses to solvency breaches using supervisory information about insurers' asset quality.     

Asymptotic results for the risk process based on marked point processes

Abstract

In this paper asymptotic properties for the risk process will be studied when the number of risk units tends to infinity. The paper extends asymptotic properties for the classical risk process to more general processes. In the classical risk process the claim amounts are assumed independent and identically distributed, and the claim number process is a homogeneous Poisson process.

The key tool is point process theory with associated martingale theory. The results are illustrated by examples.     

Are non-risk based capital requirements for insurance companies binding?

We investigate whether insurers base their solvency margins on risk factors even when operating under a supervisory regime where minimum solvency requirements do not fully take such risk factors into account. To do this, we use a dataset of about 350 Dutch insurers from all major lines of business during the pre-Solvency II period 1995–2005. We find that the levels of insurers’ actual solvency margins are related to their risk characteristics and not to regulatory solvency requirements. Consequently, the vast majority of insurers hold much more capital than required, i.e. non-risk based capital requirements generally are not binding. Requirements are found to affect solvency adjustment behaviour, though. More specifically, below-target capital ratios are raised most rapidly by those insurers whose targets are relatively close to the regulatory minimum. One implication from our results is that, because insurers already follow a risk-based approach, the transition to the new European regulatory framework, Solvency II, is likely to be smooth.     

Accounting Year Effects Modeling in the Stochastic Chain Ladder Reserving Method

Abstract

In almost all stochastic claims reserving models one assumes that accident years are independent. In practice this assumption is violated most of the time. Typical examples are claims inflation and accounting year effects that influence all accident years simultaneously. We study a Bayesian chain ladder model that allows for accounting (calendar) year effects modeling. A case study of a general liability dataset shows that such accounting year effects contribute substantially to the prediction uncertainty and therefore need a careful treatment within a risk management and solvency framework.     

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。     

Interbank Credit Lines as a Channel of Contagion

This paper assesses the potential for contagion in the Swiss interbank market using new data on bilateral bank exposures as well as on credit lines. A simulation approach is applied to assess the banking system's inherent instability. Moreover, the spill-over effects of a simulated default situation in the interbank market on the liquidity and solvency of banks are measured. The main findings are, first, that there is a substantial potential for contagion. Second, the exposure as well as the credit line contagion channel are relevant for Switzerland. Third, a lender of last resort intervention could reduce spill-over effects remarkably. Finally, the structure of the interbank market has considerable impact on its resilience against spill-over effects: Centralized markets are more prone to contagion than homogenous ones. JEL classification: C81, G21. The opinions expressed herein are my own and not those of the Swiss National Bank.     

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.     

Projections of pension fund solvency under alternative valuation regimes

This paper examines the impact of three alternative valuation regimes on perceived pension fund solvency. Deterministic valuation assumes smoothed valuation of assets and liabilities. National valuation is based on market valuation of assets and on smoothed valuation of liabilities. International valuation marks assets and liabilities to market values. Using closed-form methods based on the funding ratio return, we exemplify the dramatic effect that the choice of valuation approach has on long-horizon solvency projections.