方差保费准则下最优分红、注资和再保险策略

本文研究保险公司的最优分红、注资和再保险策略问题.保险公司可以通过再保险安排控制自身的风险暴露,它与再保险公司在方差保费准则下采用不同的参数进行费率定价.保险公司管理者也可以通过分红或注资控制公司资产,控制过程会消耗比例交易费和固定交易费.破产前分红现值与注资现值期望之差视为保险公司的价值.在最大化公司价值目标下,利用脉冲控制理论,本文找到最优的分红、注资和再保险策略及公司价值的最大值.     

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.     

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.     

有再保险控制下的非线性脉冲注资问题

假定有两家再保险公司共同接受原始保险公司的分保,且保险公司及这两家再保险公司均采用方差保费准则收取保费.基于上述跳风险模型,本文采用扩散逼近模型为基本模型来描述保险公司再保后的资产盈余.另外,为避免破产的发生,公司会接受外部资金注入.假定每次注资不低于某个固定常数d0,且有固定交易费和比例费用,即为有限制情形下的脉冲注资.本文研究最小期望折现非线性脉冲注资问题,应用Hamilton-Jacobi-Bellman(HJB)方法,给出值函数和最优策略的明晰解答.最后,对有关参数进行灵敏度分析.     

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.     

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.     

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.     

与资本市场收益变动相关的最优再保险策略

本文在假定资本市场变动与保险公司资本收益变动存在相关性的情况下,研究了保险公司最优再保险策略问题.利用HJB-变分不等方程,获得了最优再保险策略和最小破产概率的显示表达式,推广了文献[3]的结果.     

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.     

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.     

Optimal financing and dividend control of the insurance company with excess-of-loss reinsurance policy

In this paper, we consider an optimal financing and dividend control problem of an insurance company. The management of the insurance company controls the dividends payout, equity issuance and the excess-of-loss reinsurance policy. In our model, the dividends are assumed to be paid out continuously, which is of interest from the perspective of financial modeling. The objective is to find the strategy which maximizes the expected present values of the dividends payout minus the equity issuance up to the time of ruin. We solve the optimal control problem and identify the optimal strategy by constructing two categories of suboptimal control problems.     

Optimal control of the insurance company with proportional reinsurance policy under solvency constraints

This paper considers the optimal control problem of the insurance company with proportional reinsurance policy under solvency constraints. The management of the company controls the reinsurance rate and dividends payout processes to maximize the expected present value of the dividend until the time of bankruptcy. This is a mixed singular-regular control problem. However, the optimal dividend payout barrier may be too low to be acceptable. The company may be prohibited to pay dividend according to external reasons because this low dividend payout barrier will result in bankruptcy soon. Therefore, some constraints on the insurance company’s dividend policy will be imposed. One reasonable and normal constraint is that if b is the minimum dividend barrier, then the bankrupt probability should not be larger than some predetermined ε within the time horizon T. This paper is to work out the optimal control policy of the insurance company under the solvency constraints.     

Optimal control of the insurance company with proportional reinsurance policy under solvency constraints

This paper considers the optimal control problem of the insurance company with proportional reinsurance policy under solvency constraints. The management of the company controls the reinsurance rate and dividends payout processes to maximize the expected present value of the dividend until the time of bankruptcy. This is a mixed singular-regular control problem. However, the optimal dividend payout barrier may be too low to be acceptable. The company may be prohibited to pay dividend according to external reasons because this low dividend payout barrier will result in bankruptcy soon. Therefore, some constraints on the insurance company’s dividend policy will be imposed. One reasonable and normal constraint is that if $b$ is the minimum dividend barrier, then the bankrupt probability should not be larger than some predetermined $\epsilon$ within the time horizon $T$. This paper is to work out the optimal control policy of the insurance company under the solvency constraints.     

Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs

We consider an optimal impulse control problem on reinsurance, dividend and reinvestment of an insurance company. To close reality, we add fixed and proportional transaction costs to this problem. The value of the company is associated with expected present value of net dividends pay out minus the net reinvestment capitals until ruin time. We focus on non-cheap proportional reinsurance. We prove that the value function is a unique solution to associated Hamilton–Jacobi–Bellman equation, and establish the regularity property of the viscosity solution under a weak assumption. We solve the non-uniformly elliptic equation associated with the impulse control problem. Finally, we derive the value function and the optimal strategy of the control problem.     

Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs

We consider the optimal financing and dividend control problem of the insurance company with fixed and proportional transaction costs. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance process to maximize the expected present value of the dividends payout minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model with two kinds of transaction costs, which come from real financial market has been considered. We solve the mixed classical-impulse control problem by constructing two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance.     

Optimal risk control and dividend policies under excess of loss reinsurance

We study the optimal reinsurance policy and dividend distribution of an insurance company under excess of loss reinsurance. The objective of the insurer is to maximize the expected discounted dividends. We suppose that in the absence of dividend distribution, the reserve process of the insurance company follows a compound Poisson process. We first prove existence and uniqueness results for this optimization problem by using singular stochastic control methods and the theory of viscosity solutions. We then compute the optimal strategy of reinsurance, the optimal dividend strategy and the value function by solving the associated integro-differential Hamilton–Jacobi–Bellman Variational Inequality numerically.     

Optimal risk and dividend control of an insurance company with exponential premium principle and liquidation value

Assume that an insurer can control it’s surplus by paying dividends, purchasing reinsurance and injecting capital. The exponential premium principle is used when pricing insurance contract instead of the expected value principle. Under the objective of maximizing the company’s value, we identify the optimal strategies with liquidation value and transaction costs. The results illustrate that the insurer should buy less reinsurance when the surplus increases, capital injection should be considered if and only if the transaction costs and the liquidation value are relatively low, dividends are paid according to barrier strategy if the dividend rate is unrestricted or threshold strategy if the dividend rate is bounded.     

Optimality of the threshold dividend strategy for the compound Poisson model

In this paper, we consider the optimal dividend problem for the compound Poisson risk model. We assume that dividends are paid to the shareholders according to an admissible strategy with dividend rate bounded by a constant. Our objective is to find a dividend policy so as to maximize the expected discounted value of dividends until ruin. We give sufficient conditions under which the optimal strategy is of threshold type.     

Optimal control problem for an insurance surplus model with debt liability

For an insurance company with a debt liability, they could make some management actions, such as reinsurance, paying dividends, and capital injection, to balance the profitability and financial bankruptcy. Our objective is to determine risk retention rate, dividend, and capital injection strategy so as to maximize the expected discounted dividends minus the discounted cost of capital injection until the time of ruin. We assume that the dividend payments and capital injection should occur with both fixed and proportional costs. We obtain explicit expressions of the optimal value functions as well as the corresponding optimal joint strategies by routine procedures in a comprehensive basic model using a new technique to solve the related equations. Our results show that whether recapitalizing is profitable or not depends on the costs of capital raising and that the firm injects capital only when the reserves are zero and recapitalizes to the optimal reserves level if the cost of external capital is low. Copyright © 2013 John Wiley & Sons, Ltd.     

Classical and Impulse Control for the Optimization of Dividend and Proportional Reinsurance Policies with Regime Switching

We consider the optimal proportional reinsurance and dividend strategy. The surplus process is modeled by the classical compound Poisson risk model with regime switching. Considering a class of utility functions, the object of the insurer is to select the reinsurance and dividend strategy that maximizes the expected total discounted utility of the shareholders until ruin. By adapting the techniques and methods of stochastic control, we study the quasi-variational inequality for this classical and impulse control problem and establish a verification theorem. We show that the optimal value function is characterized as the unique viscosity solution of the corresponding quasi-variational inequality.