Mean-Variance Optimal Reinsurance Arrangements

Reinsurance reduces the risk but it also reduces the potential profit. The aim of the paper is to derive optimal, from the cedent's point of view, reinsurance arrangements balancing the risk measured by variance and expected profits under various mean-variance premium principles of the reinsurer. We find that quota share, excess of loss or combinations of excess of loss with quota share are the optimal rules according to a fixed expected gain of the cedent     

Optimal Reinsurance Arrangements Under Tail Risk Measures

Regulatory authorities demand insurance companies control their risk exposure by imposing stringent risk management policies. This article investigates the optimal risk management strategy of an insurance company subject to regulatory constraints. We provide optimal reinsurance contracts under different tail risk measures and analyze the impact of regulators' requirements on risk sharing in the reinsurance market. Our results underpin adverse incentives for the insurer when compulsory Value-at-Risk risk management requirements are imposed. But economic effects may vary when regulatory constraints involve other risk measures. Finally, we compare the obtained optimal designs to existing reinsurance contracts and alternative risk transfer mechanisms on the capital market.     

Unbiased premiums for Stop-Loss reinsurance

Abstract

1. Some further consideration will be given here to the problem of unbiased premium estimation for Stop-Loss reinsurance discussed by Vajda [1].     

Recursions for Distribution Functions and Stop-Loss Transforms

For any function f on the non-negative integers, we can evaluate the cumulative function o f given by o f ( s )= ~ s x=0 f ( x ) from the values of f by the recursion o f ( s )= o f ( s -1)+ f ( s ). Analogously we can use this procedure t times to evaluate the t -th order cumulative function o t f . As an alternative, in the present paper we shall derive recursions for direct evaluation of o t f when f itself satisfies a certain sort of recursion. We shall also derive recursions for the t -th order tails v t f where v f ( s )= ~ X x=s+1 f ( x ). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for f includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer's (1981). We discuss in particular convolutions and compound functions.     

Optimal Proportional Reinsurance Policies in a Dynamic Setting

We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed.     

An Extension of Arrow's Result on Optimal Reinsurance Contract

We consider the problem of finding reinsurance policies that maximize the expected utility, the stability and the survival probability of the cedent for a fixed reinsurance premium calculated according to the maximal possible claims principle. We show that the limited stop loss and the truncated stop loss are the optimal contracts.     

Catastrophe Bonds,Reinsurance, and the Optimal Collateralization of Risk Transfer

Catastrophe bonds feature full collateralization of the underlying risk transfer and thus abandon the reinsurance principle of economizing on collateral through diversification of risk transfer. Our analysis demonstrates that this feature places limits on catastrophe bond penetration, even if the structure possesses frictional cost advantages over reinsurance. However, we also show that catastrophe bonds have important uses when buyers and reinsurers cannot contract over the division of assets in the event of insolvency and, more generally, cannot write contracts with a full menu of state‐contingent payments. In this environment, segregation of collateral—in the form of multiple reinsurance companies, as well as catastrophe bond vehicles—can ameliorate inefficiencies due to reinsurance contracting constraints by improving welfare for those exposed to default risk. Numerical simulation illustrates how catastrophe bonds improve efficiency in market niches with correlated risks, or with uneven exposure of buyers to reinsurer default.     

Securitization, Insurance, and Reinsurance

This article considers strengths and weaknesses of reinsurance and securitization in managing insurable risks. Traditional reinsurance operates efficiently in managing relatively small, uncorrelated risks and in facilitating efficient information sharing between cedants and reinsurers. However, when the magnitude of potential losses and the correlation of risks increase, the efficiency of the reinsurance model breaks down, and the cost of capital may become uneconomical. At this juncture, securitization has a role to play by passing the risks along to broader capital markets. Securitization also serves as a complement for reinsurance in other ways such as facilitating regulatory arbitrage and collateralizing low-frequency risks.     

The Uses and Abuses of Finite Risk Reinsurance

Finite risk reinsurance has become the subject of investigations, litigation, and possibly new regulation. This article provides an overview of finite risk solutions and products, describing their main features and their legitimate role in helping (mainly) industrial companies manage timing, funding, and insurance risks.
Finite risk solutions generally take the form of structured insurance products designed to help companies manage risks often regarded as exotic or "tail" risks, such as environmental or asbestos liability. Although such products are underwritten by insurance or reinsurance companies, they typically involve limited risk transfer (hence the name "finite risk") while providing the insured companies with a means of pre-funding their expected losses, or what is often called "pre-loss financing." Of course, companies could choose to self-insure such risks by establishing a reserve for future losses. But finite risk provides a more credible and transparent alternative—one that reassures investors both by capping the liability and eliminating the possibility for manipulation of reserves.
Abuses of finite risk products usually concern the degree to which transactions are accounted for, disclosed, and represented to investors as achieving "significant risk transfer" when there is little or no such transfer. In the authors' words, "Users of finite should ask themselves whether the transaction helps the financial statements clearly represent the true economic income and risks of the business and, if not, then consider not doing the deal."     

再保险交易中的道德风险及其博弈分析

保险领域的道德风险,不仅仅发生在直接保险交易中,而且发生在再保险交易中.再保险交易中的道德风险,给再保险市场的发展造成了诸多危害.本文通过引入博弈论,分析了再保险交易中道德风险产生的机理,并提出了一些防范和控制的措施.     

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance.     

风险价值法及其在金融风险管理中的应用

探讨了金融工具风险价值测定的有关问题,包括风险价值的含义、金融工具风险价值测定的数理基础和具体方法等,并论述了风险价值在风险管理中的应用。     

我国再保险业面临的挑战与变革

中国的再保险业正在按照加入WTO时的承诺逐步开放。为适应由此带来的一系列深刻变化,必须加快目前较落后的保险体系建设,尽快构建一个竞争、开放、多元化发展的再保险市场体系,这包括科学定位市场模式、培育市场主体和完善制度基础等方面。     

再保险监管的国际比较及其启示

发达国家和发展中131家均根据各自的经济发展水平、所处的131际经济地位、保险业发育的程度在不同的阶段确定了不同的再保险监管重点、内容和方式方法。中国的再保险监管有着自身的特点和缺陷。应当结合再保险发展状况和再保险监管目标来选择构建我国再保险监管体系的具体措施。     

Large Sample Behavior of the CTE and VaR Estimators under Importance Sampling

Abstract

The α-level value at risk (Var) and the α-level conditional tail expectation (CTE) of a continuous random variable X are defined as its α-level quantile (denoted by q_α ) and its conditional expectation given the event {X > q_α }, respectively. Var is a popular risk measure in the banking sector, for both external and internal reporting purposes, while the CTE has recently become the risk measure of choice for insurance regulation in North America. Estimation of the CTE for company assets and liabilities is becoming an important actuarial exercise, and the size and complexity of these liabilities make inference procedures with good small sample performance very desirable. A common situation is one in which the CTE of the portfolio loss is estimated using simulated values, and in such situations use of variance reduction techniques such as importance sampling have proved to be fruitful. Construction of confidence intervals for the CTE relies on the availability of the asymptotic distribution of the normalized CTE estimator, and although such a result has been available to actuaries, it has so far been supported only by heuristics. The main goal of this paper is to provide an honest theorem establishing the convergence of the normalized CTE estimator under importance sampling to a normal distribution. In the process, we also provide a similar result for the Var estimator under importance sampling, which improves upon an earlier result. Also, through examples we motivate the practical need for such theoretical results and include simulation studies to lend insight into the sample sizes at which these asymptotic results become meaningful.     

On the Corporate Demand for Insurance: Evidence From the Global Reinsurance Market

In this article, we view the demand for reinsurance as a “special case” of the corporate demand for insurance. We analyze the extent to which reinsurance purchases by the global property–liability insurance industry vary across countries and assess the relative importance of country‐level factors compared with firm‐level factors. Using a data set consisting of 21,814 firm‐year observations from 33 (developed and developing) countries during the period 2000–2012, we find that after controlling for firm‐level factors, country‐level factors have economically as well as statistically significant effects on the demand for reinsurance.     

Reinsurance and corporate taxation in the United Kingdom life insurance industry

There are two main tax-related arguments regarding the use of reinsurance – the income volatility reduction and the income level enhancement arguments. The income volatility reduction argument contends that firms facing convex tax schedules have incentives to hedge in order to reduce the volatility of their annual taxable income and thereby lower expected tax liabilities [Smith, C.W., Stulz, R.M., 1985. Optimal hedging policies. Journal of Financial and Quantitative Analysis 19, 127–140]. The income level enhancement argument, advanced by Adiel [Adiel, R., 1996. Reinsurance and the management of regulatory ratios and taxes in the property–casualty insurance industry. Journal of Accounting and Economics 22, 207–240], is more specific to hedging via reinsurance. This perspective holds that reinsurance enhances current reported earnings via the receipt of reinsurance commissions and so increases tax liabilities. Consequently, insurance firms with high marginal tax rates should use less reinsurance than those with low marginal tax rates if tax matters. Prior studies using data on financial derivatives have produced mixed results on the validity of the first argument, while Adiel (1996) finds the second argument insignificant in his study of the use of reinsurance by a sample of United States (US) property–liability insurance firms. This study tests the two tax-related arguments using 1992–2001 data for a sample of United Kingdom (UK) life insurance firms. We find that UK life insurers with low before-planning marginal tax rates tend to use more reinsurance; in contrast, tax convexity is found to have no significant impact on the purchase of reinsurance and so the volatility-reduction argument is not supported.