风险相依下再保险双方的联合最优再保险问题

结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman(HJB)方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.     

保险公司和再保险公司之间的停止损失再保险策略选择博弈

本文在扩散逼近风险模型下考虑保险公司和再保险公司之间的停止损失再保险策略选择博弈问题.假设保险公司和再保险公司都以期望终端盈余效用增加作为购买停止损失再保险和接受承保的条件.在保险公司和再保险公司都具有指数效用函数条件下,运用动态规划原理,通过求解其对应的Hamilton-Jacobi-Bellman方程,得到了三种博弈情形下保险公司和再保险公司之间的停止损失再保险策略和值函数的显示解,以及再保险合约能够成交时再保费满足的条件.结果显示,在适当的条件下,保险公司和再保险公司之间的停止再保险合约是可以成交的.最后,通过灵敏性分析给出了最优停止损失再保险策略和再保费,以及效用损益与模型主要参数之间的关系,并给出相应的经济分析.     

汇率风险和方差保费准则下最优投资和再保险策略

假定保险公司和再保险公司都采取方差保费准则收取保费,保险公司不但可以投资本国无风险资产和风险资产,还可以投资国外的风险资产.首先我们用一几何布朗运动来刻画汇率风险,同时为了控制保险风险,假定保险公司将承担的保险业务分保给再保险公司.接着利用随机动态规划原理研究了两种情形下的最优投资和再保险问题,一种是索赔服从扩散近似模型;另一种是经典风险模型,分别得到了这两种情形下的最优投资和再保险策略,并发现汇率风险对保险公司的投资策略有很大的影响,但对再保险策略没有影响.最后对相关参数进行了敏感性分析.     

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.     

最优再保险及投资组合策略问题北大核心

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.     

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.     

净利润条件约束下拥有两类保险业务时保险公司最优再保险策略

考虑保险公司面临两类保险业务下的最优再保险问题.一类保险业务的索赔量分布波动较大,采用方差保费原理.而另一类索赔业务的索赔量分布比较集中,采用期望值保费原理.在净利润条件限制下,得到保险公司相应的最优比例和超额损失再保险策略.     

指数保费准则下的最优投资和比例再保险

该文研究了保险公司的最优投资和比例再保险问题,其中假定保险公司的盈余过程为一个带扩散扰动的经典风险过程.假定再保险的保费按照指数保费原理来计算,这使得所研究的随机控制问题成为非线性的.该文同时考虑了最大化终端财富指数效用和最大化调节系数两类问题,并给出了最优值函数和相应的最优策略的解析表达.此外,该文还分析了再保险公司的风险厌恶和保险公司的不确定性参数对最优策略的影响.     

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.     

王氏保费准则下隐含再保险公司违约风险的最优再保险设计

本文考虑到再保险公司违约风险对保险人再保险的影响,利用VaR风险度量研究最优再保险策略.在再保险合同中,再保险公司向保险人收取一定的保费,承诺赔偿再保险人面临的部分损失.但,当再保险公司承诺的限额超过其偿付能力就可能发生违约风险.因此,为了避免再保险公司违约风险,使保险公司的总风险最小,本文根据王氏保费准则,运用VaR风险度量的最优化标准,得到分层再保险是最优的,并给出相应的数值算例.     

���ʷ��պͷ����׼��������Ͷ�ʺ��ٱ��ղ���

??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.     

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.     

Optimal financing and dividend control of the insurance company with proportional reinsurance policy

We consider the optimal control problem of the insurance company with proportional reinsurance policy. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance processes to maximize the expected present value of the dividends minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model has been considered, which is more realistic. To find the solution of the mixed singular-regular control problem, we firstly construct two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance. Then we identify the value functions and the optimal strategies corresponding to the suboptimal models depending on the relationships between the coefficients.     

Robust optimal investment and reinsurance problem for a general insurance company under Heston model

In this paper, we study a robust optimal investment and reinsurance problem for a general insurance company which contains an insurer and a reinsurer. Assume that the claim process described by a Brownian motion with drift, the insurer can purchase proportional reinsurance from the reinsurer. Both the insurer and the reinsurer can invest in a financial market consisting of one risk-free asset and one risky asset whose price process is described by the Heston model. Besides, the general insurance company’s manager will search for a robust optimal investment and reinsurance strategy, since the general insurance company faces model uncertainty and its manager is ambiguity-averse in our assumption. The optimal decision is to maximize the minimal expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s surplus processes. By using techniques of stochastic control theory, we give sufficient conditions under which the closed-form expressions for the robust optimal investment and reinsurance strategies and the corresponding value function are obtained.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

基于再保险和投资的随机微分博弈

本文研究了具有再保险和投资的随机微分博弈.应用线性-二次控制的理论,在指数效用和幂效用下,求得了最优再保险策略、最优投资策略、最优市场策略和值函数的显示解,推广了文[8]的结果.通过本文的研究,当市场出现最坏的情况时,可以指导保险公司选择恰当的再保险和投资策略使自身所获得的财富最大化.     

Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth

We consider a problem of optimal reinsurance and investment with multiple risky assets for an insurance company whose surplus is governed by a linear diffusion. The insurance company’s risk can be reduced through reinsurance, while in addition the company invests its surplus in a financial market with one risk-free asset and n risky assets. In this paper, we consider the transaction costs when investing in the risky assets. Also, we use Conditional Value-at-Risk (CVaR) to control the whole risk. We consider the optimization problem of maximizing the expected exponential utility of terminal wealth and solve it by using the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Explicit expression for the optimal value function and the corresponding optimal strategies are obtained.     

Optimal dividend and dynamic reinsurance strategies with capital injections and proportional costs

We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of (cheap or non-cheap) proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they are the same as those in the model of no bankruptcy.     

索赔次数为复合Poisson-Geometric过程下的破产概率和最优投资和再保险策略

本文对索赔次数为复合Poisson-Geometric过程的风险模型,在保险公司的盈余可以投资于风险资产,以及索赔购买比例再保险的策略下,研究使得破产概率最小的最优投资和再保险策略.通过求解相应的Hamilton-Jacobi-Bellman方程,得到使得破产概率最小的最优投资和比例再保险策略,以及最小破产概率的显示表达式.     

Optimal excess-of-loss reinsurance and investment polices under the CEV model

This paper focuses on risk control problem of the insurance company in enterprise risk management. The insurer manages its financial risk through purchasing excess-of-loss reinsurance, and investing its wealth in the constant elasticity of variance stock market. We model risk process by Brownian motion with drift, and study the optimization problem of maximizing the exponential utility of terminal wealth under the controls of reinsurance and investment. Using stochastic control theory, we obtain explicit expressions for optimal polices and value function. We also show that the optimal excess-of-loss reinsurance is always better than optimal proportional reinsurance. And some numerical examples are given.