混合再保险中凸风险组合的最优再保险策略

再保险是一种有效的风险管理策略,在保险行业中扮演着至关重要的作用.本文在期望值保费原则下,考虑了再保险策略中原保险人和再保险人双方的利益,并以再保险双方各自总损失的VaR值的凸组合为目标函数,得到混合再保险中最优比例系数和最优自留额的理论解.进而,对最优解的各种情况进行了讨论和分析.本文的研究为保险公司的风险管理提供了决策依据.     

最优比例与超额损失组合再保险下的破产概率

本文站在保险人的立场上,讨论了保险公司的最优组合再保险问题.通过纯粹比例再保险,纯粹超额损失再保险,或者这两类再保险的组合方式,把保险公司的部分风险分担出去.在最大化调节系数的最优准则下,我们得出了布朗运动模型和复合Poisson模型中最优值的显示表达,并且给出了复合Poisson模型中最优策略下破产概率的最小指数上界.我们还得出结论:在一定的条件下,总存在一种纯粹超额损失再保险策略比任何一类组合再保险策略都要好.最后,通过一些数例和图表来进一步说明我们在文中所获得的结论.     

基于索赔相依的时滞均衡投资与再保险策略

本文研究保险公司的最优投资与再保险问题.假设再保险种类是比例再保险,未来索赔与历史索赔是相关的.此外,风险资产的价格过程由常方差弹性模型来描述,并且在财富过程中考虑了财富的时滞效应.在均值-方差优化准则下,本文给出了最优均衡投资和比例再保险策略及值函数的显式解.最后,通过数值分析,讨论了模型主要参数对最优策略的影响.本文所提模型及所获结果是对文献中已有研究成果的推广.     

连续时间模型下的动态随机合作再保险策略

如何通过选择再保险策略以最大化保险公司的终端期望效用是保险精算领域中的一个热门研究话题.这个问题在单期离散模型下已经有了很好的研究结果.本文首次考虑了连续时间模型下的最优动态合作再保险问题.基于互惠的再保险概念和指数效用函数,本文引入了博弈论中的Pareto最优概念,给出了含有Pareto最优合作再保险策略的核的界定方法并证明此核是非空的.通过实例,验证了合作再保险博弈的核的非空性,并且得出了在两家保险公司的情形下(保险公司和再保险公司),Pareto最优合作再保险策略是比例再保险策略.     

两类相依保险业务下基于竞争的最优再保险策略

在再保险合同制定中,保险公司与再保险公司之间是竞争的.利用相对业绩,本文量化了这种竞争.进而假设保险公司从事两类相依保险业务,在竞争下,得到了保险公司的相对财富过程.保险公司的目标是,寻找最优时间一致的再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机分析和随机控制理论,求得了最优时间一致的再保险策略和值函数的显式解,并从理论方面解释了最优解的保险和经济意义.最终,通过数值实验分析了模型参数对最优时间一致再保险策略的影响,比较了两类特殊情形与一般情形下最优再保险策略之间的关系.通过本文的研究得到了一些新的发现,研究结果可以更合理地指导保险公司的再保险决策.     

竞争与合作统一框架下的鲁棒最优再保险策略

在实际中,多个保险人之间经常存在竞争与合作.文章在竞争与合作统一框架下,研究了鲁棒最优再保险策略.每个保险人的盈余过程满足扩散逼近保险模型,n个保险人的索赔之间存在相依关系,每个保险人通过再保险减少索赔风险.文章主要的研究目标是,在最坏市场环境下,寻找最优均衡再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机动态规划和随机控制理论,求得了鲁棒最优均衡再保险策略、最优市场策略和最优值函数的显式解,并从理论上探讨了最优策略的经济意义.最终,通过数值实验分析了竞争、合作、模糊厌恶和风险厌恶对鲁棒最优均衡再保险策略的影响.文章的研究结果可以有效地指导保险人的实践.     

带相关风险的保险公司的最优分红和再保险问题

本文的研究对象是带两种相关风险业务的保险公司.本文用复合Poisson过程描述这两种风险;应用扩散逼近理论,建立了一个扩散逼近模型.利用动态再保险策略,公司可以降低其破产概率,同时通过给客户分红,公司可以保持竞争力.公司的目标是寻找最优策略和值函数来最大化期望折现分红.因为超额损失再保险策略优于比例再保险策略,所以,本文考虑公司的超额损失再保险及其分红问题.问题分两种情形讨论:分红率有界和分红率无界.在这两种情形下,本文最终得到了值函数和相应最优策略的具体表达式.     

跳-扩散风险模型的最优投资和再保险策略

本文对跳-扩散风险模型,在赔付进行比例再保险,以及盈余投资于无风险资产和风险资产的条件下,研究使得最终财富的指数期望效用最大的最优投资和比例再保险策略.得到最优投资策略和最优再保险策略,以及最大指数期望效用函数的显式表达式,发现最优策略和值函数都受到无风险利率的影响.最后通过数值计算,得到最优投资和比例再保险策略,以及值函数与模型各个参数之间的关系.     

经典风险模型下CEV股票市场中最优再保险和投资策略（英文）

本文在复合泊松跳索赔模型下,考虑保险公司投资于常弹性方差(CEV)金融市场和购买比例-超额损失组合再保险的最优策略.在期望效用最大化准则下,利用随机控制技巧,证明了,事实上,保险公司的最优再保险策略等同于要么购买一个纯超额损失再保险,要么购买一个纯比例再保险.进一步给出两种情形下的最优再保险和投资策略以及值函数的表达式.     

扩散风险模型下再保险和投资对红利的影响

对扩散风险模型,研究了比例再保险和投资对红利的影响．在常数边界分红策略下,得到了使得期望贴现红利最大的最优比例再保险和投资策略的显示表达式,并得到最大期望贴现红利的显示表达式．最后,通过数值计算得到了再保险和投资对期望红利的影响,以及最优投资策略与各参数之间的关系．     

Optimal non-life reinsurance under Solvency II Regime

The optimal reinsurance contract is investigated from the perspective of an insurer who would like to minimise its risk exposure under Solvency II. Under this regulatory framework, the insurer is exposed to the retained risk, reinsurance premium and change in the risk margin requirement as a result of reinsurance. Depending on how the risk margin corresponding to the reserve risk is calculated, two optimal reinsurance problems are formulated. We show that the optimal reinsurance policy can be in the form of two layers. Further, numerical examples illustrate that the optimal two-layer reinsurance contracts are only slightly different under these two methodologies.     

Optimality of general reinsurance contracts under CTE risk measure

By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer’s total risk. For completeness, we analyze the optimal reinsurance model under both binding and unbinding reinsurance premium constraints. By resorting to the Lagrangian approach based on the concept of directional derivative, explicit and analytical optimal solutions are obtained in each case under some mild conditions. We show that pure stop-loss ceded loss function is always optimal. More interestingly, we demonstrate that ceded loss functions, that are not always non-decreasing, could be optimal. We also show that, in some cases, it is optimal to exhaust the entire reinsurance premium budget to determine the optimal reinsurance, while in other cases, it is rational to spend less than the prescribed reinsurance premium budget.     

Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework

We study optimal reinsurance in the framework of stochastic Stackelberg differential game, in which an insurer and a reinsurer are the two players, and more specifically are considered as the follower and the leader of the Stackelberg game, respectively. An optimal reinsurance policy is determined by the Stackelberg equilibrium of the game, consisting of an optimal reinsurance strategy chosen by the insurer and an optimal reinsurance premium strategy by the reinsurer. Both the insurer and the reinsurer aim to maximize their respective mean–variance cost functionals. To overcome the time-inconsistency issue in the game, we formulate the optimization problem of each player as an embedded game and solve it via a corresponding extended Hamilton–Jacobi–Bellman equation. It is found that the Stackelberg equilibrium can be achieved by the pair of a variance reinsurance premium principle and a proportional reinsurance treaty, or that of an expected value reinsurance premium principle and an excess-of-loss reinsurance treaty. Moreover, the former optimal reinsurance policy is determined by a unique, model-free Stackelberg equilibrium; the latter one, though exists, may be non-unique and model-dependent, and depend on the tail behavior of the claim-size distribution to be more specific. Our numerical analysis provides further support for necessity of integrating the insurer and the reinsurer into a unified framework. In this regard, the stochastic Stackelberg differential reinsurance game proposed in this paper is a good candidate to achieve this goal.     

Marginal Indemnification Function formulation for optimal reinsurance

In this paper, we propose to combine the Marginal Indemnification Function (MIF) formulation and the Lagrangian dual method to solve optimal reinsurance model with distortion risk measure and distortion reinsurance premium principle. The MIF method exploits the absolute continuity of admissible indemnification functions and formulates optimal reinsurance model into a functional linear programming of determining an optimal measurable function valued over a bounded interval. The MIF method was recently introduced to analyze the reinsurance model but without premium budget constraint. In this paper, a Lagrangian dual method is applied to combine with MIF to solve for optimal reinsurance solutions under premium budget constraint. Compared with the existing literature, the proposed integrated MIF-based Lagrangian dual method provides a more technically convenient and transparent solution to the optimal reinsurance design. To demonstrate the practicality of the proposed method, analytical solution is derived on a particular reinsurance model that involves minimizing Conditional Value at Risk (a special case of distortion function) and with the reinsurance premium being determined by the inverse-S shaped distortion principle.     

基于风险调整资本收益率下的最优再保险策略

风险调整资本收益率是一个用来描述赚取收益所承担风险的重要指标,是衡量风险调整后的财务绩效的一个有效工具,在银行业中得到广泛采用。近年来,在保险公司的再保险业务中,也越来越多地采用风险调整资本收益率这一指标来衡量收益和风险。本文重新考虑了有再保险控制下的风险调整资本收益率,并得到:在一般再保险自留函数下,我们证明了分层再保险策略是最优再保险形式;进一步,我们获得了最优再保险分层水平及最优风险调整资本收益率;最后,我们也给出了算例及数值分析。     

Optimal reinsurance with regulatory initial capital and default risk

In a reinsurance contract, a reinsurer promises to pay the part of the loss faced by an insurer in exchange for receiving a reinsurance premium from the insurer. However, the reinsurer may fail to pay the promised amount when the promised amount exceeds the reinsurer’s solvency. As a seller of a reinsurance contract, the initial capital or reserve of a reinsurer should meet some regulatory requirements. We assume that the initial capital or reserve of a reinsurer is regulated by the value-at-risk (VaR) of its promised indemnity. When the promised indemnity exceeds the total of the reinsurer’s initial capital and the reinsurance premium, the reinsurer may fail to pay the promised amount or default may occur. In the presence of the regulatory initial capital and the counterparty default risk, we investigate optimal reinsurance designs from an insurer’s point of view and derive optimal reinsurance strategies that maximize the expected utility of an insurer’s terminal wealth or minimize the VaR of an insurer’s total retained risk. It turns out that optimal reinsurance strategies in the presence of the regulatory initial capital and the counterparty default risk are different both from optimal reinsurance strategies in the absence of the counterparty default risk and from optimal reinsurance strategies in the presence of the counterparty default risk but without the regulatory initial capital.     

Optimal reinsurance with premium constraint under distortion risk measures

Recently distortion risk measure has been an interesting tool for the insurer to reflect its attitude toward risk when forming the optimal reinsurance strategy. Under the distortion risk measure, this paper discusses the reinsurance design with unbinding premium constraint and the ceded loss function in a general feasible region which requiring the retained loss function to be increasing and left-continuous. Explicit solution of the optimal reinsurance strategy is obtained by introducing a premium-adjustment function. Our result has the form of layer reinsurance with the mixture of normal reinsurance strategies in each layer. Finally, to illustrate the applicability of our results, we derive the optimal reinsurance solutions with premium constraint under two special distortion risk measures—VaR and TVaR.     

A continuous-time theory of reinsurance chains

A chain of reinsurance is a hierarchical system formed by the subsequent interactions among multiple (re)insurance agents, which is quite often encountered in practice. This paper proposes a novel continuous-time framework for studying the optimal reinsurance strategies within a chain of reinsurance. The transactions between reinsurance buyers and sellers are formulated by means of Stackelberg games, in order to reflect the conflicting interests and unequal negotiation powers in the bargaining process. Assuming the variance premium principle and the mean–variance criterion on the surplus processes, we solve the time-consistent optimal reinsurance demands and pricing strategies in explicit forms, which are surprisingly plain.Based on the proposed reinsurance chain models, our in-depth theoretical analysis shows that: (a.) it is optimal to situate more (resp. less) risk averse reinsurers to the latter (resp. former) positions in a chain of reinsurance; (b.) adding new reinsurers will lower the reinsurance prices at all levels in a chain of reinsurance, promoting the existing agents to rationally control their respective risk exposures; and essentially (c.) alleviate the systemic risk in the chain structure.     

Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria

This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer.Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.     

保险公司的最优投资与一般再保险策略

本文研究了在股票价格服从几何布朗运动的假设下,原保公司考虑再保险时的最优投资问题.运用动态规划和鞅方法,得到了一般最优控制问题所满足的HJB方程以及该方程的识别定理,并分别对比例再保险和超额再保险做了详细分析.