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The purpose of this paper is to analyze the optimal reinsurance contract structure from the crop insurer's perspective.

A very powerful and flexible empirical‐based reinsurance model is used to analyze the optimal form of the reinsurance treaty. The reinsurance model is calibrated to unique data sets, including private reinsurance experience for Manitoba, and loss cost ratio (LCR) experience for all of Canada, under the assumption of the standard deviation premium principle and conditional tail expectation risk measure.

The Vasicek distribution is found to provide the best statistical fit for the Canadian LCR data, and the empirical reinsurance model stipulates that a layer reinsurance contract structure is optimal, which is consistent with market practice.

While the empirical reinsurance model is able to reproduce the optimal shape of the reinsurance treaty, the model produces some inconsistencies between the implied and observed attachment points. Future research will continue to explore the reinsurance model that will best recover the observed market practice.

Private reinsurance premiums can account for a significant portion of a crop insurer's budget, therefore, this study should be useful for crop insurance companies to achieve efficiencies and improve their risk management.

To the best of the authors' knowledge, this is the first paper to show how a crop insurance firm can optimally select a reinsurance contract structure that minimizes its total risk exposure, considering the total losses retained by the insurer, as well as the reinsurance premium paid to private reinsurers.

The purpose of this paper is to introduce a new probability density function having both unbounded and bounded support with a wider applicability. While the distribution with bounded support on [0, 1] has applications in insurance and inventory management with ability to fit risk management data on proportions better than existing bounded distributions, the same with unbounded support is used as a lifetime model and is considered as an attractive alternative to some existing models in the reliability literature.

The new density function, called modified exponential-geometric distribution is derived from the exponential-geometric distribution introduced by Adamidis and Loukas (1998). The support of the density function is shown to be both unbounded and bounded depending on the values of one of the shape parameters. Various properties of the density function are studied in detail and the parameters are estimated through maximum likelihood method of estimation. A number of applications related to reliability, insurance and inventory management are exhibited along with some useful data analysis.

A single probability distribution with both unbounded and bounded support, which does not seem to exist in the reliability literature, is introduced in this paper. The proposed density function exhibits varying shapes including U-shape, and the failure rate also shows increasing, decreasing and bathtub shapes. The Monte Carlo simulation shows that the estimates of the parameters are quite stable with low standard errors. The distribution with unbounded support is shown to have competitive features for lifetime modeling through analysis of two data sets. The distribution with bounded support on [0, 1] is shown to have application in insurance and inventory management and is found to t data on proportions related to risk management better than some existing bounded distributions.

The authors introduce an innovative probability distribution which contributes significantly in insurance and inventory management besides its remarkable statistical and reliability properties.

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.

Few issues in business ethics are as polarizing as the practice of risk classification and underwriting in the insurance industry. Theorists who approach the issue from a background in economics often start from the assumption that policy-holders should be charged a rate that reflects the expected loss that they bring to the insurance scheme. Yet theorists who approach the question from a background in philosophy or civil rights law often begin with a presumption against so-called “actuarially fair” premiums and in favor of “community rating,” in which everyone is charged the same price. This paper begins by examining and rejecting the three primary arguments that have been given to show that actuarially fair premiums are unjust. It then considers the two primary arguments that have been offered by those who wish to defend the practice of risk classification. These arguments overshoot their target, by requiring a “freedom to underwrite” that is much greater than the level of freedom enjoyed in most other commercial transactions. The paper concludes by presenting a defense of a more limited right to underwrite, one that grants the legitimacy of the central principle of risk classification, but permits specific deviations from that ideal when other important social goods are at stake.

This article discusses issues common to the pricing of both insurance and finance. These include increasing collaboration between insurance companies and banks, deregulation of various insurance and finance markets, integrated risk management, and the emergence of financial engineering as a new profession. Rather than attempting to give an exhaustive exposition of the issues at hand, the author highlights developments that, from a methodological point of view, offer new insight into the comparison of pricing mechanisms between insurance and finance.

Definitions of pooling effects in insurance companies may convey the impression that the achieved risk reduction effect will be beneficial for policyholders, since typically lower premiums are paid for the same safety level with an increasing number of insureds, or a higher safety level is achieved for a given premium level for all pool members. However, this view is misleading and the purpose of this paper is to reexamine this apparent merit of pooling from the policyholder's perspective.

This is achieved by comparing several valuation approaches for the policyholders' claims using different assumptions of the individual policyholder's ability to replicate the contract's cash flows and claims.

The paper shows that the two considered definitions of risk pooling do not offer insight into the question of whether pooling is actually beneficial for policyholders.

The paper contributes to the literature by extending and combining previous work, focusing on the merits of pooling claims (using the two definitions above) from the policyholder's perspective using different valuation approaches.

This article examines how reinsurance coupled with new financial instruments can expand coverage to areas exposed to catastrophe losses from natural disasters, and demonstrates how reinsurance and the catastrophe‐linked financial instruments can be combined to lower the price of protection from its current level. A simple example illustrates the relative advantages and disadvantages of pure catastrophic bonds and pure indemnity reinsurance in supporting a structure of payments contingent on certain extreme events occurring. The authors suggest ways to combine these two instruments using customized catastrophe indices to expand coverage and reduce the cost of protection. This article states six principles for designing catastrophic risk transfer systems and discusses practical issues for implementation, and then concludes with suggestions for future research.

The purpose of this paper is to analyse the determinants of workers’ compensation insurance prices in Portugal.

Multiple regression analysis was used to study the insurance price determinants. The independent variables considered are: payroll, number of employees, and incidence rate. In addition, three categorical variables were used: region, classification of economic activities, and enterprise size. A cross-firm panel data sample from the SABI database of 1,435 firms was considered, over a time horizon from 2010 to 2012. Furthermore, the sample split criterion was the enterprise size.

As expected, the results suggest that payroll and number of employees are related with workers’ compensation insurance prices. Furthermore, incidence rate, region, type of economic activities, and enterprise size have a positive and significant influence on premiums.

More panel data are needed to allow a greater focus on the impacts of GDP fluctuations and sectoral consolidation on insurance pricing. Further research could also include the impact of capital/reserving cycles, which can be driven both by economic shocks and the competition cycle. It is well known that insurers tend to reduce reserving standards when under pressure, and this can result in inadequate pricing.

The process of workers’ compensation insurance price formation is disentangled. The results suggest that the workers’ compensation insurance premiums behave as expected, especially under periods of economic strain. Therefore, workers’ compensation rate regulation should take this evidence into account, specifically through the establishment of minimum rates, which will protect the insurer, the employer, and the employees alike.

The paper is part of a considerable literature on insurance pricing in workers’ compensation, most of which has centred on private markets in the USA. This paper is the first empirical work that employs private market data for Portugal.

In financial planning, customers are typically confronted with choosing a premium payment scheme when investing in a mutual fund, which is often equipped with an investment guarantee to provide downside protection. Guarantee costs may thereby also be charged differently depending on the provider. The paper aims to investigate the impact of the premium payment method on different performance measures for a mutual fund with an investment guarantee.

The paper compares a fund with annual and upfront premiums as well as constant guarantee costs versus the guarantee price as an annual percentage fee of the fund value, always ensuring that the present value of premium payments is the same for all product variants. The paper further studies the relevance of the guarantee level and the contract term.

The results emphasize that even though the present value of premiums paid into the contract is the same, the type of premium (upfront versus annual) as well as the type of guarantee cost (upfront versus annual fee) has a considerable impact on the performance.

Providers can thus make a product more attractive for consumers by individually adjusting the premium scheme depending on their preferences and by making the resulting risk-return-profile transparent, while keeping the other contract characteristics unchanged (e.g. extent of the guarantee).

To date, there has been no comprehensive analysis with specific focus on the impact of different premium payment schemes (in particular with respect to savings premiums and guarantee costs) on risk and return of a mutual fund with otherwise given contract characteristics such as the underlying fund strategy and the investment guarantee, even though the premium scheme itself can already have a considerable impact on the terminal payoff distribution and thus risk-return profiles. In addition, such an analysis can provide important information for consumers and providers in designing and choosing attractive products by simply adjusting the premium scheme (if possible) instead of or in addition to changing other product features.

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。