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This article aims to examine the risk inherent in the insurance of the aviation industry, to take an outsider's look at those risks and to develop certain “capital market” pricing rules.

The aviation industry presents a classic low‐frequency/high‐limit insurance problem. Pricing such exposures is difficult because of the high degree of uncertainty involved. After a review of the considerations that an insurance underwriter traditionally brings to the problem, the author applies a simple pricing rule incorporating current thinking on risk evaluation.

The results of the author's approach are compared with the results of traditional pricing rules, generating interesting insights. The application of the new methodology to the analysis of current pricing and of alternative proposals is suggested.

The article will be of value to those interested in the aviation industry and in the pricing of insurance and reinsurance.

Catastrophe (CAT) events associated with natural catastrophes and man-made disasters cause profound impacts on the insurance industry. This research thus reviews the impact of CAT risk on the insurance industry and how traditional reinsurance and securitized risk-transfer instruments are used for managing CAT risk.

This research reviews the impact of CAT risk on the insurance industry and how traditional reinsurance and securitized risk-transfer instruments are used for managing CAT risk. Apart from many negative influences, CAT events can increase the net revenue of the insurance industry around CAT events and improve insurance demand over the post-CAT periods. The underwriting cycle of reinsurance causes inefficiencies in transferring CAT risks. Securitized risk-transfer instruments resolve some inefficiencies of the reinsurance market, but are subject to moral hazard, basis risk, credit risk, regulatory uncertainty, etc. The authors introduce some popular securitized solutions and use Merton's structural framework to demonstrate how to value these CAT-linked securities. The hybrid solutions by combining reinsurance with securitized CAT instruments are expected to offer promising applications for CAT risk management.

The authors introduce some popular securitized solutions and use Merton's structural framework to demonstrate how to value these CAT-linked securities. The hybrid solutions by combining reinsurance with securitized CAT instruments are expected to offer promising applications for CAT risk management.

This research reviews a broad array of impacts of CAT risks on the (re)insurance industry. CAT events challenge (re)insurance capacity and influence insurers' supply decisions and reconstruction costs in the aftermath of catastrophes. While losses from natural catastrophes are the primary threat to property–casualty insurers, the mortality risk posed by influenza pandemics is a leading CAT risk for life insurers. At the same time, natural catastrophes and man-made disasters cause distinct impacts on (re)insures. Man-made disasters can increase the correlation between insurance stocks and the overall market, and natural catastrophes reduce the above correlation. It should be noted that huge CAT losses can also improve (re)insurance demand during the postevent period and thus bring long-term effects to the (re)insurance industry.

The purpose of this paper is to provide a detailed analysis of industry loss warranties (ILWs), an alternative risk transfer instrument which has become increasingly popular throughout the last few years.

The authors first point out key characteristics of ILWs important to investor and cedent, including transaction costs, moral hazard, basis risk, counterparty risk, industry loss index, and regulation. Next, the authors present and discuss the adequacy of actuarial and financial approaches for pricing ILWs, as well as the aspects of basis risk. Finally, drivers of demand and associated models frameworks from the purchaser's viewpoint are studied.

Financial pricing approaches for ILWs are highly sensitive to input parameters, which is important given the high volatility of the underlying loss index. In addition, the underlying assumption of replicability of the claims is not without problems. Due to their simple and standardized structure and the dependence on a transparent industry loss index, ILWs are low‐barrier products, which can also be offered by hedge funds. In principle, traditional reinsurance contracts are still preferred as a measure of risk transfer, especially since these are widely accepted for solvency capital reduction. However, the main important impact factor for the demand of ILWs from the perspective of market participants, i.e. large diversified reinsurers and hedge funds, is the lower price due to rather low transaction costs and less documentation effort. Hence, ILWs are attractive despite the introduction of basis risk and the still somewhat opaque regulatory environment.

An important issue for future research is how reinsureds deal with the basis risk inherent in ILWs. Another central point is the development of a European industry loss index and the creation of an exchange platform to enable an even higher degree of standardization and a faster processing of transactions.

ILWs feature an industry loss index to be triggered, and, in some cases, a double‐trigger design that includes a company indemnity trigger. ILW contracts belong to the class of alternative risk transfer instruments that have become increasingly popular, especially in the retrocession reinsurance market. There has been no comprehensive analysis of these instruments in academic literature to date. Consequently, the authors believe that this paper provides a high degree of originality.

The authors consider the mutual benefits of the ceding company and reinsurance company in the design of reinsurance contracts. Two objective functions to maximize social expected utilities are established, which are to maximize the sum of the expected utilities of both the ceding company and reinsurance company, and to maximize their products. The first objective function, additive, emphasizes the total gains of both parties, while the second, multiplicative, accounts for the degree of substitution of gains of one party through the loss of the other party. The optimal price and retention of reinsurance are found by a grid search method, and numerical analysis is conducted. The results indicate that the optimal solutions for two objective functions are quite different. However, optimal solutions are sensitive to the change of the means and volatilities of the claim loss for both objective functions. The results are potentially valuable to insurance regulators and government entities acting as reinsurers of last resort.

In this paper, the authors apply relatively simple, but in the view significant, methods and models to discuss the optimization of excess loss reinsurance strategy. The authors only consider the influence of loss distribution on optimal retention and reinsurance price but neglect the investment factor. The authors also consider the benefits of both ceding company and reinsurance company to determine optimal premium and retention of reinsurance jointly based on maximizing social utility: the sum (or the product) of expected utilities of reinsurance company and ceding company. The authors solve for optimal solutions numerically, applying simulation.

This paper establishes two optimization models of excess-of-loss reinsurance contract against catastrophic losses to determine optimal premium and retention. One model considers the sum of the expected utilities of a ceding company and a reinsurance company's expected utility; another considers the product of them. With an example, the authors find the optimal solutions of premium and retention of excess loss reinsurance. Finally, the authors carry out the sensitivity analysis. The results show that increasing the means and the volatilities of claim loss will increase the optimal retention and premium. For objective function I, increasing the coefficients of risk aversion of or reducing the coefficients of risk aversion of will make the optimal retention reduced but the optimal premium increased, and vice versa. However, for objective function 2, the change of coefficient of risk aversion has no effect on optimal solutions.

Utility of the two partners: The ceding company and the reinsurance company, may have different weights and different significance. The authors have not studied their relative significance. The simulation approach in numerical methods limits us to the probability distributions and stochastic processes the authors use, based on, generally speaking, lognormal models of rates of return. This may need to be generalized to other returns, including possible models of shocks through jump processes.

In the recent two decades, reinsurance companies have played a great role in hedging mega-catastrophic losses. For example, reinsurance companies (and special loss sharing arrangements) paid as much as two-thirds of the insured losses for the September 11, 2001 tragedy. Furthermore, large catastrophic events have increased the role of governments and regulators as reinsurers of last resort. The authors hope that the authors provide guidance for possible balancing of the needs of two counterparties to reinsurance contracts.

Nearly all governments around the world are engaged in regulation of insurance and reinsurance, and some are reinsurers themselves. The authors provide guidance for them in these activities.

The authors believe this paper to be a completely new and original contribution in the area, by providing models for balancing the utility to the ceding insurance company and the reinsurance company.

我們探討分出公司和再保險公司在再保險合約的設計上、如何能達至互利互惠。研究確立了兩個目標函數，分別為把分出公司和再保險公司兩者之預期效用的總和最大化，以及把它們的產品最佳化。第一個目標函數是加法的，強調兩個參與方的總增益;而第二個目標函數則是乘法的，這個目標函數，闡釋參與方因另一方虧損而有所收益之取代度。再保險的最佳價格和自留額是利用網格搜索法找出的，數值分析也予以進行。研究結果顯示，兩個目標函數的最佳解決方案甚為不同。唯最佳解決方案會對就這兩個目標函數而言的追討損失的波動、以及其平均值之改變產生敏感反應。研究結果將會見其價值於作為在萬不得已的時候的再保險人的保險業規管機構和政府實體。

在這學術論文裡，我們採用了相對簡單、但我們認為是重要的方法和模型，來探討超額賠款再保險策略的優化課題。我們只考慮虧損分佈對最佳自留額和再保險價格的影響，而不去檢視投資因素。我們亦考慮對分出公司和再保險公司兩者的利益，來釐定最佳保費和再保險的自留額，而這兩者則共同建基於把社會效益最大化之上：再保險公司和分出公司的預期效益的總和 (或其積數) 。 我們採用類比模仿方法、來解決尋求在數字上最佳解決方案的問題。

本研究建立了就應對嚴重虧損而設的兩個超額賠款再保險合約的優化模型，來釐定最佳的保費和自留額。其中一個模型考慮了分出公司和再保險公司兩者各自的預期效益的總和。另外的一個模型則考慮了兩者的預期效益的積數。透過例子，我們找到了保費和超額虧損再保險自留額的最佳解決方案。最後，我們進行了敏感度分析。研究結果顯示、若增加追討損失的平均值和波動，則最佳自留額和保費也會隨之而增加。就第一個目標函數而言，若增加風險規避係數、或減少這個係數，則最佳自留額會隨之而減少，但最佳保費卻會隨之而增加，反之亦然。唯就第二個目標函數而言，風險規避係數的改變，對最佳解決方案是沒有影響的。

• – 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

• – 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

– 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

– 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

在過去20年裡，再保險公司在控制極嚴重災難性的損失上曾扮演重要的角色。例如、再保險公司 (以及特殊的損失分擔安排) 為了2001年9月11日的災難事件而支付多至保險損失的三分之二的費用。而且，重大的災難性事件使政府及作為最後出路再保險人的調控者得扮演更重要的角色。我們希望研究結果能為再保險合約兩對手提供指導，以平衡雙方的需要。

全球差不多每個政府都參與保險和再保險的管理工作，有部份更加本身就是再保險人。研究結果為他們的管理工作提供了指導。

我們相信本學術論文、提供了平衡分出保險公司和再保險公司效用性的模型，就此而言，本論文在相關的領域上作出了全新和獨創性的貢獻。

The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework.

The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixture distribution is proposed. A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR, and information from the observed data of the individual region/province is integrated with the collective experience of the entire crop reinsurance program in Canada.

A comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR's is more conservative, and provides a more scientific approach to enhance the reinsurance pricing.

Credibility models are in the early stages of application in the area of agriculture insurance, therefore, the credibility models presented in this paper could be verified with data from other geographical regions.

The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks.

This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Bühlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.

This study is designed to investigate how the use of reinsurance affects the primary insurers' profitability and pricing on their insurance products.

This study examines the impact of reinsurance on the insurers’ profitability using a two stage least square to control the endogeneity problem with a reinsurance variable. The study analyzes 11,894 firm-year observations between 2001 and 2009.

The study finds that the use of reinsurance in general has a negative impact on property/casualty insurers' performance. However, reinsurance obtained from affiliated firms has a positive impact on profitability, which supports the existence of internal capital markets in the insurance industry.

The finding of study implies that reinsurance transactions are used among affiliated insurers for not only managing underwriting risk and increasing underwriting capacity but also subsidizing capital through internal capital markets. In term of limitation, due to the availability of price data, this study uses only one insurance cycle of 9 years, albeit not weakening the findings.

Especially for non-affiliated insurers, the finding suggests that they need to find an alternative way to transfer underwriting risk without having to use costly reinsurance.

This paper directly investigates the impact of reinsurance utilization on insurers' profitability and pricing.

The purpose of this paper is to propose an improved reinsurance pricing framework, which includes a crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. A yield restatement approach to account for changing crop mix through time is also demonstrated.

The new crop yield forecasting model is empirically analyzed based on detailed farm-level data from Manitoba, Canada, covering 216 crop varieties from 19,238 farms from 1996 to 2011. As well, corresponding weather data from 30 stations, including daily temperature and precipitation, are considered. Algorithms that combine screening regression, cross-validation and principal component analysis are evaluated for the purpose of achieving efficient dimension reduction and model selection.

The results show that the new yield forecasting model provides significant improvements over the classical regression model, both in terms of in-sample and out-of-sample forecasting abilities.

The empirical analysis is limited to data from the province of Manitoba, Canada, and other regions may show different results.

This research is useful from a risk management perspective for insurers and reinsurers, and the framework may also be used to develop improved weather risk management strategies to help manage adverse weather events.

This is the first paper to integrate a credibility estimator for crop yield forecasting, and develop a closed form reinsurance pricing formula.

This article aims to examine the existence of an underwriting cycle in property‐liability insurance for France, Germany and Switzerland (primary markets) and for the European reinsurance industry. It is also aimed to test how the two markets are related with each other in each country and how they influence each other.

Loss ratio data for France, Germany and Switzerland are used for the recent period 1982‐2001 in connection with the price of reinsurance in Europe as well as the money market rate. To test for the existence of cycles and calculate their length auto‐regressive processes of second order are applied.

There are cross‐country differences for the primary markets of the three countries. The reinsurance price index is highly cyclical with a calculated cycle length of almost nine years. It is shown that the reinsurance price index has a strong influence on the primary market loss ratios of the three countries studied.

With the exception of two studies examining the impact of reinsurance on insurance prices and profits, there has been no research as yet to determine the role of reinsurance on the cyclical behavior of underwriting results. This gap is filled here by an empirical study on three European countries.

Insurance‐linked securities can benefit both issuers and investors; they supply insurance and reinsurance companies with additional risk capital at reasonable prices (with little or no credit risk), and supply excess returns to investors that are uncorrelated with the returns of other financial assets. This article explains the terminology of insurance and reinsurance, the structure of insurance‐linked securities, and provides an overview of major transactions. First, there is a discussion of how stochastic catastrophe modeling has been applied to assess the risk of natural catastrophes, including the reliability and validation of the risk models. Second, the authors compare the risk‐adjusted returns of recent securitizations on the basis of relative value. Compared with high‐yield bonds, catastrophe (“CAT”) bonds have wide spreads and very attractive Sharpe ratios. In fact, the risk‐adjusted returns on CAT bonds dominate high‐yield bonds. Furthermore, since natural catastrophe risk is essentially uncorrelated with market risk, high expected excess returns make CAT bonds high‐alpha assets. The authors illustrate this point and show that a relatively small allocation of insurance‐linked securities within a fixed income portfolio can enhance the expected return and simultaneously decrease risk, without significantly changing the skewness and kurtosis of the return distribution.

Property and casualty (“P&C”) insurance companies rely on “risk capital” to absorb large losses that unexpectedly deplete claims‐paying resources and reduce underwriting capacity. The purpose of this paper is to review the similarities and differences between two different types of risk capital raised by insurers to cover losses arising from natural catastrophes: internal risk capital provided by investors in insurance company debt and equity; and external risk capital provided by third parties. The paper also explores the distinctions between four types of external catastrophe risk capital: reinsurance, industry loss warranties, catastrophe derivatives, and insurance‐linked securities. Finally, how the credit crisis has impacted alternative sources of catastrophe risk capital in different ways is considered.

The discussion is based on the conceptual framework for analyzing risk capital developed by Merton and Perold.

In 2008, the P&C insurance industry was adversely affected by significant natural catastrophe‐related losses, floundering investments, and limited access to capital markets, all of which put upward pressure on catastrophe reinsurance premiums. But the influx of new risk capital that generally accompanies hardening markets has been slower than usual to occur in the wake of the credit crisis. Meanwhile, disparities between the relative costs and benefits of alternative sources of catastrophe risk capital are even more pronounced than usual.

Although many insurance companies focus on how much reinsurance to buy, this paper emphasizes that a more important question is how much risk capital to acquire from external parties (and in what form) vis‐à‐vis investors in the insurance company's own securities.