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Demonstrates the feasibility of, and introduces a practical approach to enhancing, reinsurance efficiency using index‐based instruments.

First reviews the general mathematical framework of reinsurance optimization. Next, illustrates how index‐based instruments can potentially enhance reinsurance efficiency through a simple yet self‐contained example. The simplicity allows the analytical examination of the cost and benefits of an index‐based contract. Finally, introduces a real‐world model that optimizes index‐based reinsurance instruments using the genetic algorithm.

Identifies the key factors that determine the efficiency of index‐based reinsurance contracts and demonstrates that, in the property catastrophe reinsurance market, the combined effect of these factors frequently allows the construction of an index‐based hedging program that is more efficient than a traditional excess‐of‐loss reinsurance contract. A robust optimization model based on the genetic algorithm is introduced and shown to be effective in optimizing index‐based reinsurance contracts.

Most financial optimization procedures are subject to parameter risk, which can adversely affect the robustness of their solutions. The reinsurance optimization approach presented in this paper is not completely immune from this problem. It remains a challenging problem for actuarial researchers and practitioners.

The concept and method proposed in this paper can be applied to designing real‐world reinsurance programs.

This paper makes two contributions to the risk finance literature: a systematic approach for evaluating the costs and benefits of index‐based reinsurance instruments, and an innovative and practical model for optimizing reinsurance efficiency.

Purpose: This chapter is based on risk management of the insurance sector with reinsurance as its linchpin. Such is the importance of the insurance sector that its risk management must be considered.

Need for the study: Risk management of various sectors is gaining much attention. The insurance sector, known to manage the risk of multiple sectors, also requires its own chance to be controlled with the same or even more intensity. Considering the importance of reinsurance coupled with the dependency of primary insurers on reinsurers and the absence of research on reinsurers, the need to conduct a comprehensive study on the topic is felt.

Methodology: It will be a conceptual chapter based on the rigorous literature on the topic integrated with the researcher’s insights to bring forth the framework of reinsurers for the readers.

Findings: It is found that insurers can themselves become the victims of the financial crisis in case they insure risks that surpass their economic boundaries. Not only this, the failure of insurance companies can have a ripple effect on the country’s economy. Therefore, insurers must possess financial resilience; to remain so, they need to have prudent management of the risk they are undertaking.

Practical implications: The study covers a relatively less researched area of reinsurance and hence has a vast scope of research in the future. The study would be helpful to stakeholders like regulators and primary insurers. It will unveil the paradigm of reinsurance and enlighten the stakeholders on how to use it effectively.

The usual, simple and computationally expensive recovery payment method for a given reinsurance treaty, besides the total run-off triangle, builds a new run-off triangle, say recovery run-off triangle, for the reinsurer’s contribution and predicts the reinsurer’s contribution to the total loss reserves. This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties.

The authors propose a new solution to the problem of how to consider reserving issues when there is a reinsurance treaty for a portfolio of general insurance policies. Considering this when determining pricing or making capital decisions is very important.

In particular, it considers the quota share (QS) treaty, surplus (SPL) treaty, excess-of-loss (XL) treaty, largest claims reinsurance (LCR) treaty and excédent du coût moyen relatif (ECOMOR) treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the mean square error of prediction (MSEP). The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study.

This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties. In particular, it considers the QS treaty, SPL treaty, XL treaty, LCR treaty and ECOMOR treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the MSEP. The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study.

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。

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 article is to investigate the impact of counterparty risk on the basis risk of industry loss warranties as well as on reinsurance with and without collateral under different dependence structures. The authors additionally compare the solvency and Sharpe ratio for different premium loadings and contract parameters.

The authors propose a model framework extension to account for the counterparty risk of risk transfer arrangements. Copulas are used to also take into account non-linear dependencies between risk factors, and Monte Carlo simulation is employed to derive numerical results and to conduct sensitivity analyses.

The authors show that the impact of counterparty risk is particularly pronounced for higher degrees of dependencies and tail dependent losses, i.e. in cases of basis risk levels that appear low if counterparty risk is not considered. With respect to counterparty risk management, the authors find that already partial collateralization limits counterparty and basis risk to more acceptable levels.

The study results are particularly relevant to practitioners, as insurers may not only underestimate the “true” basis risk of index-linked instruments, but also the effect of counterparty risk of reinsurance contracts along with the consequences for solvency and profitability.

The authors extend existing literature by allowing for the (partial) default of industry loss warranties and reinsurance under different dependence structures. Furthermore, the authors include profitability in addition to risk considerations. The interaction effects between counterparty risk and the basis risk of index-based alternative risk transfer instruments are largely unstudied, despite their considerable relevance in practice.

The purpose of this paper is to test for the existence of residual moral hazard in the three largest US reinsurance markets over the period 1995‐2000 and examine the effectiveness of retention limit, experience rating and long‐term contracting relationship in controlling for moral hazard.

This paper focuses on one peculiar feature in the insurance industry, group affiliation, and tests the presence of residual moral hazard in reinsurance markets. This approach may enable moral hazard to be separated from adverse selection. Moreover, two different econometric methods are employed for the empirical tests: the non‐parametric matching estimators method and the parametric fixed effects model, which may enhance the robustness of the results.

The author finds that, over the period 1995‐2000, residual moral hazard does not exist in the private passenger auto liability and product liability reinsurance markets, but might exist in the homeowners reinsurance market. This finding suggests that the US reinsurance markets are efficient overall and moral hazard is not a serious issue over this period of time. In addition, the author finds that retention limit is effectively used by reinsurers to mitigate the moral hazard problem, whereas experience rating and long‐term contracting relationship are either not used or not effective in controlling the loss experience of reinsurance.

US reinsurance markets are efficient overall and moral hazard is not a serious issue.

The significance of this paper is multifaceted. First, it investigates moral hazard in reinsurance markets by examining internal and external reinsurance jointly. Second, instead of directly examining the correlation between risk and coverage, this paper tests for the presence of residual moral hazard in reinsurance markets. Moreover, the author employs two different econometric methods: the non‐parametric matching estimators method and the parametric fixed effects model, which may enhance the robustness of the results. Third, the use of panel data makes it possible to explore the roles of retention limit, experience rating and long‐term contracting relationship in mitigating the moral hazard problem.

This paper aims to examine the relationship between geographical diversification and the underwriting performance for the world's largest reinsurance groups. It also aims to verify that the form and nature of the relationship between diversification and performance follow an S‐shaped curve with increased diversification of the largest reinsurance groups.

Analysis in the paper is based on the concept of Geographical Spread Index defined and calculated by UNCTAD. Data on largest reinsurance groups in the world are published annually by Standard & Poor's for only a limited number of reinsurance groups. To overcome the small sample problem, a re‐sampling procedure from the original sample, similar to a bootstrap sample, is used to validate the results.

The results show that, overall, international geographical diversification has a positive effect on a reinsurance firm's underwriting performance but that this relationship is not linear. It rather follows an S‐shaped curve. Although data limitation does not allow more sophisticated investigations, the results reported in this paper are nevertheless significant. It seems that at an early stage of expansion in proximate markets there are efficiency gains for the firm. With increased internationalization there may be a diminution in performance because of higher transaction costs or learning costs for new markets. Further expansion in foreign markets brings back efficiency and higher performance.

Only cross‐section data for a small sample of companies are available and therefore it is not possible to analyze the dynamics of geographical diversification. A firm may deliberately expand for long‐term strategy reasons such as market share even though this is detrimental to medium‐run performance. Also, the analysis cannot provide any answer to the existence or not of a maximum level of international diversification beyond which performance would decline.

In the literature on firm diversification in the financial services sector, product diversification and performance has received significant attention with mixed results but except for a few papers, the internationalization aspect has not been examined. The reinsurance sector is important since reinsurance activities are, by nature, more geographically diversified than other financial activities. Furthermore, the largest European reinsurance groups dominate this worldwide market and many reinsurance companies have, in the past decade, increased their foreign direct investment and acquired other companies in part because of the belief that only very large players will have the cost advantages necessary to remain competitive in global markets.

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.

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.