Optimal proportional reinsurance under dependent risks

This paper considers a correlated risk model with thinning-dependence structure.The authors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional reinsurance under mean variance principle for the proposed model.The authors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.     

Optimal investment and proportional reinsurance in the Sparre Andersen model

From the insurer’s point of view,this paper studies the optimal investment and proportional reinsurance in the Sparre Andersen model.Under the criterion of maximizing the adjustment coefficient, the authors obtain the closed form expressions of the optimal strategy and the maximal adjustment coefficient,and derive the explicit expression of the ruin probability or its lower bound when the claim sizes are exponentially distributed.Some numerical examples are presented,which show the impact of model parameters on the optimal values.It can also be seen that the optimal strategy to maximize the adjustment coefficient is sometimes equivalent to those which minimize the ruin probability.     

比例再保险模型的最优控制策略研究

在对一类带分红过程的比例再保险模型进行分析的过程中，不但把保险公司与再保公司在交易过程中需支付的交易费用考虑进去，而且还考虑了公司破产时的补偿值这一重要因素，以此为基础建立了一种新的模型，从而弥补了传统模型的不足．为使公司获得最大的风险回报，针对不同的市场参数，对此新模型进行了详尽的技术分析，给出了不同情形下所应采取的最优控制策略，得出了相应的最大风险回报函数．     

Optimal reinsurance and investment strategies for insurers with regime-switching and state-dependent utility function

This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer, where price processes of the risky assets and wealth process of the insurer are both described by Markovian regime switching. The target of the insurer is assumed to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function. By employing the dynamic programming approach, the optimal value functions and the optimal reinsurance-investment strategies are derived. In addition, the impact of some parameters on the optimal strategies and the optimal value functions is analyzed, and lots of interesting results are discovered, such as the conclusion that excess-of-loss reinsurance is better than proportional reinsurance is not held in the regime-switching jump-diffusion model.     

保险公司的最优再保险和红利分配

本文将讨论保险公司的最优再保险和分红策略。其中风险由复合泊松过程描述了,相应的盈余过程（ｓｕｒｐｌｕｓ ｐｒｏｃｅｓｓ）是一个跳跃过程。对这一跳跃过程最优控制问题,我们应用动态规划原理得到了积分－微分（ｉｎｔｅｇｒｏ－ｄｉｆｆｅｒｅｎｔｉａｌ）形式的ＨＪＢ方程。由于此方程的解析解较难得到,我们将采用近似方法,将模型在时间和状态空间上分别离散化,将离散最优控制问题的解作为连续模型的近似。     

Optimal combinational of quota-share and stop-loss reinsurance contracts under VaR and CTE with a constrained reinsurance premium

This paper considers the problem of minimizing the VaR and CTE of an insurer’s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, the authors give the explicit reinsurance forms and the minimal VaR and CTE of retained risk in the case of quota-share after stop-loss reinsurance and the case of stop-loss after-quota-share reinsurance respectively. Finally, the authors conclude that the quota-share after stop-loss is a better reinsurance strategy than stop-loss after quota-share to minimize the VaR and CTE with a same constrained reinsurance premium. And the pure stop-loss reinsurance is preferred for an insurer with a high level regulatory requirement.     

Optimal control using microscopic models for a pollutant elimination problem

Optimal control problem with partial derivative equation (PDE) constraint is a numerical-wise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman (HJB) equation approximation. For solving the problem, only an HJB equation (a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.     

基于内部竞争的金融企业的最优风险管理

讨论了金融企业的最优管理问题,金融企业的目标是：用于(股东)分红的净收益的期望现值最大,根据Bellman最优性原理,得出了分红情况下的Bellman方程,通过对所得方程的分析给出了解析解和最优控制策略．文章首次提出了最大容忍损失和临界破产概率两个概念,据此给出了破产概率新的解法并得到了企业的临界破产概率和破产原因．     

周期风险模型下的保险基金最优投资研究

考虑周期风险模型下保险人的最优投资问题.假设保险人可投资于多种风险资产,投资目标是最大化风险过程的调节系数.当风险资产的价格过程服从几何布朗运动时,采用鞅方法给出保险人破产概率的指数型上界,得到了最优投资策略的解析解.最后根据国内股票市场的实际数据进行了实证分析.     

带有持续扰动非线性系统的最优跟踪控制

研究具有外界持续扰动的非线性系统的无静差最优跟踪控制问题。首先基于内模原理构造一扰动补偿器,将系统化为无扰动的增广系统。然后利用灵敏度法推导出了该系统的最优跟踪控制律。仿真实例表明了该设计方法的有效性。     

不确定时滞反应扩散系统的滑动模控制

借助不等式分析方法研究一类不确定时滞反应扩散系统的滑动模控制问题,设计了滑模控制器。分析了在滑动模切换面上滑动模控制系统关于不确定量的不变性特征,为研究在系统工作环境的变化、降阶近似、线性化近似、测量误差等因素干扰下所建立的实际控制系统的数学模型———不确定时滞分布参数控制系统的鲁棒性问题奠定了理论基础。     

Optimal pricing,production, and sales policies for new product under supply constraint

This paper considers a firm that sells a durable product with a given market potential. The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.     

地球同步卫星的小推力离轨最优控制

地球同步卫星结束服务时,需要离开地球同步轨道。考虑利用小推力的方式使得地球同步卫星离轨。将小推力的最优控制问题考虑为一个平面轨道转移问题,利用最优控制理论建立两点边值问题求解轨道转移问题,并给出数值计算结果。     

具有控制约束的不确定离散系统最优保性能控制

对一类具有范数有界时变参数不确定性和控制输入约束的离散时间线性系统,采用线性矩阵不等式处理方法,导出了保性能控制律存在的条件,证明了该条件等价于一组线性矩阵不等式的可行性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。进而,通过建立并求解一个凸优化问题,给出了具有控制约束的不确定离散系统最优保性能控制律设计方法。     

Optimal dividend strategies in the diffusion model with stochastic return on investments

This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher (2007), we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.     

扩散过程下单因素利率模型的统一框架

利用随机微积分等数学方法，在考虑利率的变动服从扩散过程的前提下，推导出一个单因素利率期限结构模型的统一分析框架，然后在这一杠架下具体分析比较了几个常用的模型，并且利用这一框架通过数值仿真例子探讨了利率风险的度量，最后从总体上探讨了单因素模型的优缺点及改进方向。     

Optimal inverse LQG control for certain ode and PDE stationary processes

<正> Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional systems;in particular a class of PDE systems of elliptic type.These systems arestudied in the now familiar framework developed by J.L.Lions and E.Magenes,specialized to asubclass of such systems important in a variety of applications.As an extended example this paperstudies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation,presenting both analytic and computational work related to such problems.     

Optimal closed-loop identification test design for internal model control

In this paper, optimal cloeed-loop test design for control is studied. The identified model is used for controller design. The control scheme used is internal model control (IMC) and the design constraint is the power of the process output or that of the reference signal. The measure of performance is the variance of the error between the output of the ideal closed-loop system (with the ideal controller) and that of the actual closed-loop system (with the controller computed from the identified model). Optimal spectrum formulae can be used to determine the PRBS signal in industrious identification.     

货架空间分配和库存控制联合优化策略研究

研究了需求率受展示空间影响的零售商品的货架空间分配和库存控制联合决策问题.针对各物品单独补货和多物品共同补货两种不同策略,分别建立了联合决策模型,分析了最优解的特性,并给出了共同补货模型的遍历搜索算法和两种近似求解算法.数值仿真研究表明:改进近似算法几乎达到了遍历搜索算法的效果,而近似算法在保证较好计算效果的基础上大大提高了计算效率;多物品共同补货与各物品单独补货策略相比,不仅改变了零售商的订购计划,也影响了其货架空间分配策略,并使零售商减少了库存,增加了利润;该模型也为零售商提供了比一些经验做法更优的货架空间分配策略.     

损失厌恶下带有风险约束的委托投资组合模型

在管理者呈损失厌恶的假设下,构建了带有风险约束的委托投资组合模型,研究委托投资管理中的最优投资问题.通过构造辅助函数将以条件风险价值为约束的委托投资组合问题转化为约束含有随机凸函数的随机优化问题,证明了最优策略的存在性.进而利用随机抽样方法构造了Monte Carlo罚函数算法,得到了近似最优投资策略,并证明了当样本容量足够大时近似最优投资策略几乎处处是原委托投资组合问题的最优策略.最后,给出了数值算例说明模型的有效性和管理者的损失厌恶对最优策略的影响.