New Risk-Based Capital Standards in the European Union: A Proposal Based on Empirical Data

In response to criticism concerning the current solvency system, the European Commission is developing new rules for insurance companies operating in the member states of the European Union (EU). Under this so-called Solvency II concept, an insurer is allowed to verify its solvency by using an internal risk management model previously approved by the regulatory authority. In this article we develop such an internal risk management approach for property-liability insurers that is based on dynamic financial analysis (DFA). The proposed concept uses a simulation technique and models the central risk factors from the investment and underwriting areas of an insurance company. On the basis of the data provided by a German insurer, the ruin probabilities under different scenarios and varying planning horizons are calculated.     

Contingent Commissions and the Management of the Independent Agency

Insurance agencies continue to exist as an important distribution mechanism because they give their contracting insurers advantages in risk selection and enable insurance applicants to transfer complex risks. While independent agencies are compensated by upfront commissions, a key component of their profitability is tied to contingent commissions. A contingency arrangement represents ex post compensation normally tied to underwriting profitability, volume, and annual growth. We report two actual contingency contracts in the context of a decision process for choosing among contingency offerings by insurers. We incorporate both uncertainty and correlation among key variables to arrive at values for competing contracts, then use a downside risk approach that helps agency owners select the better contract. The approach offered in this article is scalable to a selection problem for any number of contingency arrangements.     

On the probability of ruin in the collective risk theory for insurance enterprises with oly negative risk sums

Abstract

1. The determination of the probability that an insurance company once in the future will be brought to ruin is a problem of great interest in insurance mathematics. If we know this probability, it does not only give us a possibility to estimate the stability of the insurance company, but we may also decide which precautions, in the form of f. ex. reinsurance and loading of the premiums, should be taken in order to make the probability of ruin so small that in practice no ruin is to be feared.     

On the Possibility of Profitable Self-Selection Contracts in Competitive Insurance Markets

Several studies extend the Rothschild–Stiglitz model of competitive insurance contracting with adverse selection by incorporating additional dimensions of private information and conclude that some insurers may earn positive profit in a separating, self-selection equilibrium, provided each insurer is restricted to making a single contract offer. The main result of this article is that these profitable configurations are not sustainable when individual insurers can offer multiple contracts. It is also shown that the ability to offer multiple contracts overturns equilibria that have applicants from different risk classes pooled as well as those where profits are dissipated by a fixed entry cost.     

Ruin probabilities and optimal capital allocation for heterogeneous life annuity portfolios

A large part of the actuarial literature is devoted to the derivation of ruin probabilities in various non-life insurance risk models. On the contrary, very few papers deal with ruin probabilities for life insurance portfolios. The difficulties arise from the dependence and non-stationarity of the annual payments made by the insurance company. This paper shows that the ruin probability in case of life annuity portfolios can be computed from algorithms derived by De Pril (1989) and Dhaene & Vandebroek (1995). Approximations for ruin probabilities are discussed. The present article complements the works of Frostig et al. (2003) who considered whole life, endowment, and temporary assurances, and of Denuit & Frostig (2008) who considered homogeneous life annuities portfolios. Here, heterogeneous portfolios (with respect to age and/or face amounts) are studied. Particular attention is paid to the capital allocation problem. The total amount of reserve is shared among the risk classes in order to minimize the ruin probability. It is then fair to charge a higher margin to the risk classes requiring more capital.     

On the Lack of Participating Policy Usage by Stock Insurance Companies

Stock insurers can reduce or eliminate agency conflicts between policyholders and stockholders by issuing participating insurance. Despite this benefit, most stock companies don't offer participating contracts. This study explains why. We study an equilibrium with both stock and mutual insurers in which stockholders set premiums to provide a fair expected return on their investment, and with a policyholder who chooses the insurance contract that maximizes her expected utility. We demonstrate that stockholders cannot profitably offer fully participating contracts, but can profitably offer partially participating insurance. However, when the policyholder participation fraction is high, the fair‐return premium is so large that the policyholder always prefers fully participating insurance from the mutual company. Policies with lower levels of policyholder participation are optimal for policyholders with relatively high risk aversion, though such policies are usually prohibited by insurance legislation. Thus, the reason stock insurers rarely issue participating contracts isn't because the potential benefits are small or unimportant. Rather, profitability or regulatory constraints simply prevent stock insurers from exercising those benefits in equilibrium.     

“Social Security-Adequacy,Equity, and Progressiveness: A Review of Criteria Based on Experience in Canada and the United States,” Robert L. Brown and Jeffrey Ip,January 2000

Abstract

We consider an optimal dynamic control problem for an insurance company with opportunities of proportional reinsurance and investment. The company can purchase proportional reinsurance to reduce its risk level and invest its surplus in a financial market that has a Black-Scholes risky asset and a risk-free asset. When investing in the risk-free asset, three practical borrowing constraints are studied individually: (B1) the borrowing rate is higher than lending (saving) rate, (B2) the dollar amount borrowed is no more than K > 0, and (B3) the proportion of the borrowed amount to the surplus level is no more than k > 0. Under each of the constraints, the objective is to minimize the probability of ruin. Classical stochastic control theory is applied to solve the problem. Specifically, the minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations, and their associated optimal reinsurance-investment policies are found by verification techniques.     

Optimal constrained investment in the Cramer-Lundberg model

We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk-free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when short-selling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. For example, for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum, or with the case of no short-selling and no borrowing studied in Azcue and Muler.     

Price Regulation in Property-Liability Insurance: A Contingent-Claims Approach

A discrete-time option-pricing model is used to derive the “fair” rate of return for the property-liability insurance firm. The rationale for the use of this model is that the financial claims of shareholders, policyholders, and tax authorities can be modeled as European options written on the income generated by the insurer's asset portfolio. This portfolio consists mostly of traded financial assets and is therefore relatively easy to value. By setting the value of the shareholders' option equal to the initial surplus, an implicit solution for the fair insurance price may be derived. Unlike previous insurance regulatory models, this approach addresses the ruin probability of the insurer, as well as nonlinear tax effects.     

Impact of Underwriting Cycles on the Solvency of an Insurance Company

Abstract

This paper studies the solvency of an insurance firm in the presence of underwriting cycles. A small or medium-size insurance company with a price-taker position in the market is considered. Its premium income is assumed to obey an autoregressive process with cycles. Specifically, the premium income for a specific calendar year is influenced by the market experience for the last couple years. Under this classical AR(2) dynamics governing the premium income, an explicit expression for the ultimate ruin probability is derived, using a martingale approach, in the lighttailed claims case. Furthermore, the logarithmic asymptotic behavior of the ultimate ruin probability as well as the typical path to ruin are investigated. Then a comparison is made with the classical case where the same company operates on a market without such cycles. Asymptotically, the presence of market cycles is shown to increase the risk for the company. Numerical illustrations are performed on Canadian motor insurance market data and support the theoretical analysis.     

Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.     

The drivers and value of enterprise risk management: evidence from ERM ratings

In the course of recent regulatory developments, holistic enterprise-wide risk management (ERM) frameworks have become increasingly relevant for insurance companies. The aim of this paper is to contribute to the literature by analyzing determinants (firm characteristics) as well as the impact of ERM on the shareholder value of European insurers using the Standard & Poor’s ERM rating to identify ERM activities. This has not been done so far, even though it is of high relevance against the background of the introduction of Solvency II, which requires a holistic approach to risk management. Results show a significant positive impact of ERM on firm value for the case of European insurers. In particular, we find that insurers with a high quality risk management (RM) system exhibit a Tobin’s Q that on average is about 6.5% higher than for insurers with less high quality RM after controlling for covariates and endogeneity bias.     

Ruin under stochastic dependence between premium and claim arrivals

We investigate, focusing on the ruin probability, an adaptation of the Cramér–Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of the premiums and of the claims respectively, are independent. Such a model exhibits a stochastic dependence between the aggregate premium and claim amount processes. An explicit expression for the ruin probability is obtained when the claim and premium sizes are exponentially distributed.     

Regulatory capital and asset risk transfer

We explore whether life insurers use a unique reinsurance arrangement to manage assets tied to their regulatory capital. Typical reinsurance allows insurers to reduce their regulatory capital by transferring liabilities (reserves), and the associated assets, to reinsurers. With modified coinsurance (ModCo), insurers maintain control of their liabilities and assets while transferring regulatory capital requirements to the reinsurer. Holding fixed an insurer's reported capital, we find that ModCo allows insurers to report higher risk-based capital ratios. Insurers with ModCo are less likely to fire sale downgraded bonds. We also find suggestive evidence of regulatory arbitrage, as most ModCo is purchased from reinsurers in countries with low capital requirements or within the same insurance group.     

Considerations of cost trade-offs in insurance solvency surveillance policy

We propose a process for identifying potentially insolvent insurers on a cost-effective basis. A loss cost function is developed such that the effectiveness of monitoring is maximized relative to a cost constraint. The loss cost function is supported by a model that provides a rank ordering of financial institutions according to their probability of insolvency. When tested against a full sample of property-liability insurance companies , the procedure provides information critical to maximizing the effectiveness of regulatory resources available for solvency surveillance and performs well as a predictor of insolvency. Likewise, the rank ordering of insurers overcomes an estimation problem critical to establishing risk-adjusted guaranty assessments.     

中国的“影子保险”:来自监管自然实验的证据

影子保险在金融稳定中扮演着重要角色,但现有文献较多关注影子银行,对影子保险关注不足。“影子保险”即保险公司通过再保险方式将保险业务转移给不受监管或者受监管较弱的关联企业的活动,这会推高其真实的杠杆水平,增加金融体系脆弱性。然而,由于影子保险的不透明性和缺少自然实验,现有研究仅基于有限数据或模型给出简单的特征事实或结构性估计,很少能从因果关系上清楚地识别影子保险活动及其机制。本文利用中国加强对中资保险公司(处理组)再保险关联交易监管的政策冲击这一自然实验,使用微观数据和双重差分方法,识别了中国金融体系中的影子保险活动。研究发现,相关监管有效降低了影子保险活动,这一效应对集团公司的影响尤为显著;在机制方面,相关监管通过影响中资保险公司资产负债表两端的结构性调整进而降低了其风险承担行为,提高了经营稳定性。本文方法对识别金融机构的监管套利和防范系统性金融风险具有一定参考意义。     

Parisian ruin probability with a lower ultimate bankrupt barrier

The paper deals with a ruin problem, where there is a Parisian delay and a lower ultimate bankrupt barrier. In this problem, we will say that a risk process get ruined when it stays below zero longer than a fixed amount of time ζ > 0 or goes below a fixed level ?a. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we identify the Laplace transform of the ruin probability in terms of so-called q-scale functions. We find its Cramér-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples.     

Should I Stay or Should I Go? The Impact of Natural Disasters and Regulation on U.S. Property Insurers’ Supply Decisions

In this article, we identify the main factors that drive insurers’ willingness to offer coverage in catastrophe‐prone property insurance lines. We compare insurers’ supply decisions in personal and commercial lines, with an emphasis on insurers’ responses in the aftermath of natural disasters. Our empirical results suggest important policy implications with regard to improving the availability of insurance against catastrophic threats. Concerning the impact of regulatory constraints, we present empirical evidence that certain regulatory responses may unintentionally impede insurers’ willingness to provide coverage against natural disasters.     

The Capital Structure of Firms Subject to Price Regulation: Evidence from the Insurance Industry

Automobile and workers' compensation insurance are relatively homogeneous products sold under varying regulatory systems among the states. This paper investigates how price regulation affects the capital structure decisions of profit-maximizing insurers who sell insurance in both competitive and/or regulated markets. Specifically, we test the hypothesis that insurers subject to price regulation will choose to hold less capital. In addition, we hypothesize insurers subject to more stringent regulatory pricing constraints will choose even higher degrees of leverage because the benefits of holding additional amounts of capital are suppressed. We conduct empirical tests using cross-sectional data on insurers and find evidence consistent with both hypotheses. These findings have important implications for insurance price and solvency regulation. Stricter price regulation increases the default risk (i.e., reduces the financial quality) of insurance contracts purchased by individuals and firms.