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     

Reinsurance Arrangements Maximizing Insurer's Survival Probability

The article concerns the problem of purchasing a reinsurance policy that maximizes the survival probability of the insurer. Explicit forms of the contracts optimal for the insurer are derived which are stop loss or truncated stop loss depending on the initial surplus, a quota to be spend on reinsurance and pricing rules of both the insurer and the reinsurer.     

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.     

The Tail Stein's Identity with Applications to Risk Measures

In this article, we examine a generalized version of an identity made famous by Stein, who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works followed to extend the lemma to the larger class of elliptical distributions. The lemma has had many applications in statistics, finance, insurance, and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is very important in actuarial science and insurance. Our article therefore introduces the concept of the “tail Stein's identity” to the case of any random variable defined on an appropriate probability space with a Lebesgue density function satisfying certain regularity conditions. We also examine this “tail Stein's identity” to the class of discrete distributions. This extended identity allows us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This holds a large promise for applications in risk management.     

Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability

A reinsurance treaty involves two parties, an insurer and a reinsurer. The two parties have conflicting interests. Most existing optimal reinsurance treaties only consider the interest of one party. In this article, we consider the interests of both insurers and reinsurers and study the joint survival and profitable probabilities of insurers and reinsurers. We design the optimal reinsurance contracts that maximize the joint survival probability and the joint profitable probability. We first establish sufficient and necessary conditions for the existence of the optimal reinsurance retentions for the quota‐share reinsurance and the stop‐loss reinsurance under expected value reinsurance premium principle. We then derive sufficient conditions for the existence of the optimal reinsurance treaties in a wide class of reinsurance policies and under a general reinsurance premium principle. These conditions enable one to design optimal reinsurance contracts in different forms and under different premium principles. As applications, we design an optimal reinsurance contract in the form of a quota‐share reinsurance under the variance principle and an optimal reinsurance treaty in the form of a limited stop‐loss reinsurance under the expected value principle.     

保险公司最优投资及再保险策略

在最大化生存概率和最大化终止时蒯期望效用准则下,通过求解相应的HJB方程,获得了最优投资策略以及最优比例再保险策略的闭式解.这一研究结果易于实时操作,对投资者的决策有直接的指导意义.     

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Abstract

We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.     

Optimal Reinsurance Design: A Mean-Variance Approach

In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results.     

最优再保险的两类定价模型

针对停止损失再保险(stop loss reinsurance)，分别运用均值一方差(mean-variance)保费定价原理及效用理论(utility theory)，在再保险人总索赔额的基础之上推导出最优再保险(optimal reinsurance)的保费定价模型。     

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.     

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."     

再保险业的风险管理探析

再保险业的风险特性决定了它是一个风险程度高、专业性强的领域，实施科学有效的风险管理是再保险企业经营活动的关键环节。因此，对完善的再保险企业风险管理系统的组成部分及其主要内容、对再保险业风险管理的主要技术手段进行了详细分析介绍。     

VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance

Abstract

It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.     

BT模式下商业银行贷款的风险及其防范

“财富黑马”严介和以及他的太平洋建设集团一直都是业界关注的焦点。然而该公司最近频频遭遇多家银行逼债,公司及严介和本人能被冻结的财产已经被多家法院重复冻结数次,我们不禁要问,太平洋究竟怎么了?本文追根溯源,系统分析了太平洋集团赖以生存的BT模式及其特点,并对BT项目融资模式下商业银行贷款面临的风险及相关防范措施进行了深入探讨。     

新形势下企业财务风险的控制方法研究

在界定财务风险涵义的基础上,分析了新形势下财务风险的形成原因。认为财务管理环境的变化是产生新的财务风险的外部原因;财务管理系统功能不强、环境适应能力差是产生新的财务风险的内部原因。并在此探讨的基础上提出了以强化系统功能为目标的财务风险防范措施。     

再保险业务组合风险的实证分析

为了充分反映再保险业务线之间的相依性结构以及由此而产生的风险分散化效应,本文用完全正相关假设及学生t联接函数的3种形式来评估一个再保险组合的风险价值(VaR)和尾部条件预期(TCE),认为联接函数的选择对多业务线保险公司的资本需求和分散性效应都有明显影响。学生t类联接函数能够灵活反映多业务线之间相依性的联接函数,随着自由度的变化,可以模拟损失分布之间的不同相依性结构。     

尾部风险研究进展与评述

由于部分业务、部门或市场的尾部风险溢出不仅会引发金融体系的“多米诺骨牌”效应,而且会对实体经济产生巨大负外部性,因此尾部风险事件极易引起金融市场震荡。鉴于此,识别与监测尾部风险是有效防控系统性金融风险爆发与传染的起点。本文首先以全球金融危机为节点,根据文献厘清尾部风险测度指标在危机前后的脉络。其次,介绍与尾部风险传染密切相关的尾部风险相依、金融关联网络的相关研究进展,在此基础上对尾部风险溢出强度及溢出方向展开讨论。再次,本文归纳了引发尾部风险溢出的宏观、中观和微观层面的影响因素以及尾部风险管理的路径选择。最后,对当前及未来尾部风险相关研究进行评述与展望。据此,力求为我国进一步提高防范化解金融风险能力、统筹推进疫情防控和经济社会发展、促进国民经济稳健运行和良性循环提供借鉴。     

Measuring Investment Risk Based on Tail Thickness

In recent years, both institutional andindividual investors have come to rely heavilyupon techniques for analyzing (defining andmeasuring) risk. In this respect, the issue thatcontinues to require the attention of academicresearchers and practitioners alike is how toconcisely define investment risk and, moreimportantly, how to best measure it. Selecting anappropriate risk definition involves trade-offsamong ease of measurement, forecast ability, andintuition of individual investors. The purpose ofthis paper is to present an alternative index formeasuring unconditional (or total) risk. Theproposed measure reflects behavior in general, andthickness in particular, of the lower tail of thedistribution of returns. We therefore argue itprovides a more useful and reasonable indexbecause, unlike measures frequently used, itsestimation depends upon the most relevant datafrom the sample distribution. We describe riskanalysis based on lower tail behavior and identifyits advantages over existing methods. Finally,using data of weekly returns to the CREF StockFund, we provide an empirical example toillustrate the technique.