基于投资的我国再保险预测性定价新探讨

从系统的观点出发,把保险公司的赔付情况与投资收益结合,对非比例再保险建立在一类在较弱的市场假设条件下进行投资的线性正倒向随机微分方程的改进模型.根据一类特殊线性倒向随机微分方程的显式解,加入时间序列预测方法,给出了基于投资的非比例再保险定价公式,为保险公司厘定非比例再保险的保费提供新的可行性方法.     

投资影响下的再保险策略

本文研究了投资影响下的再保险策略,利用有关的线性正倒向随机微分方程,获得投资影响下再保险的自留比例或自留额的计算式子.     

Poisson-Geometric模型下时间一致的最优再保险-投资策略选择

本文研究Poisson-Geometric模型下,时间一致的再保险-投资策略选择问题.在风险模型中,理赔发生次数用Poisson-Geometric过程描述,保险公司在进行再保险时,按照方差值原理计算再保险的保费.保险人在金融市场上投资时,风险资产满足带跳的随机微分方程.保险人的目标是,选择一个时间一致的再保险-投资策略,最大化终止时刻财富的均值同时最小化其方差.通过使用随机控制理论,求得时间一致的再保险-投资策略以及值函数的显式解.最后分析结果的经济意义,并通过数值计算,解释了模型参数对最优策略的影响.     

CEV模型下时滞最优投资与再保险问题

在常方差弹性（constant elasticity of variance,CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

带交易费用的最优投资和比例再保险

研究了保险公司的最优投资和再保险问题.保险公司的盈余通过跳-扩散风险模型来模拟,可以把盈余的一部分投资到金融市场,金融市场由一个无风险资产和n个风险资产组成,并且保险公司还可以购买比例再保险;在买卖风险资产时,考虑了交易费用.通过随机控制的理论,获得了最优策略和值函数的显示解.     

考虑交易费用和债务的再保险和投资问题

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题. 假设保险公司本身有着一定的债务, 债务的多少服从线性扩散方程. 保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险. 资产中风险资产的价格波动服从几何布朗运动, 其债务多少的演化也是依据布朗运动而上下波动. 该文考虑了风险资产与债务之间的相互关系, 考虑了在进行风险投资时的交易费用, 并且利用HJB方程求得保险公司的最大最终资产的预期指数效用, 给出了相应的最优价值函数和最优策略的数值解.     

CEV模型下最大化HARA效用的最优再保险与投资策略

在风险资产价格服从CEV模型时,考虑保险公司为最大化双曲绝对风险厌恶(HARA)效用的最优投资与再保险问题.假定保险公司的索赔过程为带漂移的布朗运动,且保险公司通过购买比例再保险来转移索赔风险,运用随机控制理论和Legendre变换方法得到了最优策略的显示表达式.     

最优再保险及投资组合策略问题

为规避风险的巨大波动,保险公司会将承保的理赔进行分保,即再保险.假定再保险公司采用方差保费准则从保险公司收取保费.应用扩散逼近模型,刻画了保险公司有再保险控制下的资本盈余.另外,保险公司的盈余允许投资到利率、股票等金融市场.通过控制再保险及投资组合策略,研究了最小破产概率.应用动态规划方法(Hamilton-Jacobi-Bellman方程),对最小破产概率、最优再保险及投资组合策略给出了明晰解答,并给出了数值直观分析.     

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.     

具有随机保费和交易费用的最优投资-再保险策略

本文研究具有随机保费和交易费用的最优投资和再保险策略选择问题.保险公司的盈余通过跳-扩散过程来模拟,假设保费收入是随机的.我们的研究目标是寻找一个最优再保险和投资策略,最大化投资终止时刻财富的期望效用.应用随机控制理论,我们得到最优投资-再保险策略和值函数的显式解.通过数值计算,我们给出模型参数对最优策略的影响.结果揭示了一些令人感兴趣的现象,它们可以对实际中的再保险和投资予以指导.     

溢额再保险定价模型

再保险定价方法以随机过程为基础,与传统的以概率统计为基础的再保险定价方法有明显的不同,它不用考虑死亡率,损失的概率分布等因素,针对溢额再保险,建立了其定价的随机微分方程,给出了具体的定价表达式.     

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??Under inflation influence, this paper investigate a stochastic differential game with reinsurance and investment. Insurance company chose a strategy to minimizing the variance of the final wealth, and the financial markets as a game ``virtual hand' chosen a probability measure represents the economic ``environment' to maximize the variance of the final wealth. Through this double game between the insurance companies and the financial markets, get optimal portfolio strategies. When investing, we consider inflation, the method of dealing with inflation is: Firstly, the inflation is converted to the risky assets, and then constructs the wealth process. Through change the original based on the mean-variance criteria stochastic differential game into unrestricted cases, then application linear-quadratic control theory obtain optimal reinsurance strategy and investment strategy and optimal market strategy as well as the closed form expression of efficient frontier are obtained; finally get reinsurance strategy and optimal investment strategy and optimal market strategy as well as the closed form expression of efficient frontier for the original stochastic differential game.     

基于时滞效应的随机微分投资与比例再保险博弈

金融市场不断发展,激烈的市场竞争使得相对绩效比较在保险机构的业绩评估中占据越来越重要的地位。考虑历史业绩对公司决策的影响,引入时滞效应,研究时滞效应对具有竞争关系公司之间最优投资策略和最优再保险策略的影响。运用随机最优控制和微分博弈理论,针对Cramér-Lundberg模型,得到了均衡投资和再保险策略,给出了值函数的显式解;然后进一步针对近似扩散过程,求得指数效用下均衡投资策略和比例再保险策略的显式表达。通过数值算例,分析了最优均衡策略随模型各重要参数的动态变化。结论显示:保险公司在决策时是否将时滞信息纳入考虑之中将大大影响其投资和再保险行为。保险公司考虑较早时间财富值越多,其投资再保险行为就表现得越趋向于保守和谨慎;与之相反,如果保险公司对行业间的竞争越看重,其投资再保险策略就越倾向于冒险和激进。     

How retention levels influence the variability of the total risk under reinsurance

Recently, Escudero and Ortega (Insur. Math. Econ. 43:255–262, 2008) have considered an extension of the largest claims reinsurance with arbitrary random retention levels. They have analyzed the effect of some dependencies on the Laplace transform of the retained total claim amount. In this note, we study how dependencies influence the variability of the retained and the reinsured total claim amount, under excess-loss and stop-loss reinsurance policies, with stochastic retention levels. Stochastic directional convexity properties, variability orderings, and bounds for the retained and the reinsured total risk are given. Some examples on the calculation of bounds for stop-loss premiums (i.e., the expected value of the reinsured total risk under this treaty) and for net premiums for the cedent company under excess-loss, and complementary results on convex comparisons of discounted values of benefits for the insurer from a portfolio with risks having random policy limits (deductibles) are derived.      

考虑时滞效应与均值-方差效用的非零和投资与再保险博弈

在考虑时滞效应的影响下研究了非零和随机微分投资与再保险博弈问题。以最大化终端绝对财富和相对财富的均值-方差效用为目标,构建了两个相互竞争的保险公司之间的非零和投资与再保险博弈模型,分别在经典风险模型和近似扩散风险模型下探讨了博弈的Nash均衡策略。借助随机控制理论以及相应的广义Hamilton-Jacobi-Bellman（HJB）方程,得到了均衡投资与再保险策略和值函数的显式表达。最后,通过数值例子分析了模型中相关参数变动对均衡策略的影响。     

A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers

In this work, we study the equilibrium reinsurance/new business and investment strategy for mean–variance insurers with constant risk aversion. The insurers are allowed to purchase proportional reinsurance, acquire new business and invest in a financial market, where the surplus of the insurers is assumed to follow a jump–diffusion model and the financial market consists of one riskless asset and a multiple risky assets whose price processes are driven by Poisson random measures and independent Brownian motions. By using a version of the stochastic maximum principle approach, we characterize the open loop equilibrium strategies via a stochastic system which consists of a flow of forward–backward stochastic differential equations (FBSDEs in short) and an equilibrium condition. Then by decoupling the flow of FSBDEs, an explicit representation of an equilibrium solution is derived as well as its corresponding objective function value.     

Optimal Investment-Reinsurance Strategy with Exchange Rate Risk under Variance Premium Principl

It is assumed that both an insurance company and a reinsurance company adopt the variance premium principle to collect premiums. Specifically, an insurance company is allowed to investment not only in a domestic risk-free asset and a risky asset, but also in a foreign risky asset. Firstly, we use a geometry Brownian motion to model the exchange rate risk, and assume that the insurance company could control the insurance risk by transferring the insurance business into the reinsurance company. Secondly, the stochastic dynamic programming principle is used to study the optimal investment and reinsurance problems in two situations. The first is a diffusion approximation risk model and the second is a classical risk model. The optimal investment and reinsurance strategies are obtained under these two situations. We also show that the exchange rate risk has a great impact on the insurance company's investment strategies, but has no effect on the reinsurance strategies. Finally, a sensitivity analysis of some parameters is provided.     

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??It is assumed that both an insurance company and a reinsurance company adopt the variance premium principle to collect premiums. Specifically, an insurance company is allowed to investment not only in a domestic risk-free asset and a risky asset, but also in a foreign risky asset. Firstly, we use a geometry Brownian motion to model the exchange rate risk, and assume that the insurance company could control the insurance risk by transferring the insurance business into the reinsurance company. Secondly, the stochastic dynamic programming principle is used to study the optimal investment and reinsurance problems in two situations. The first is a diffusion approximation risk model and the second is a classical risk model. The optimal investment and reinsurance strategies are obtained under these two situations. We also show that the exchange rate risk has a great impact on the insurance company's investment strategies, but has no effect on the reinsurance strategies. Finally, a sensitivity analysis of some parameters is provided.