The Optimal Dividend Barrier in the Perturbed Compound Poisson Risk Model with Randomized Observation Time

This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend.In this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived.When the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained.Finally,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.     

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．     

随机保费下带红利的期望贴现惩罚函数

利用Gerber—Shiu期望贴现惩罚函数统一研究了在保费随机到达和红利边界下的破产问题，推广了Albrecher,Kainholer（2002）和Bao Zhen—hua（2006）中的结论。首先本文考虑了索赔到达间隔服从普通概率分布时的期望贴现惩罚函数，并得到无红利边界时的极限解；再将红利边界固定为常数，考虑了平稳更新过程和PH更新过程中的结果。最后本文将结论应用于破产概率、破产前盈余的概率分布及破产前盈余过程到达红利边界的概率等实例，并进行了数值实现。     

基于时间不一致性偏好与扩散模型的最优分红策略

本文考虑具有时间不一致性偏好的企业管理者的最优分红策略.假定企业盈余资金由一般扩散模型描述,管理者的偏好由准双曲贴现函数刻画,目标是最大化破产前的累积红利现值.基于管理者对自己未来偏好的认识,分别考虑幼稚型和成熟型管理者的最优分红策略.首先利用随机最优控制方法,得到了两类管理者优化问题的HJB方程及验证定理.然后以常系数扩散模型为例,得到幼稚型与成熟型管理者的最优分红策略及最优值函数的解析式,并对分红策略进行了敏感性分析.结果表明常系数扩散模型下具有时间不一致性偏好的管理者倾向于提前分红,其中成熟型管理者比幼稚型管理者更倾向于发放红利;此外,通过对幼稚型与成熟型管理者施加合适的破产惩罚,可使得幼稚型与成熟型管理者的最优策略与无破产惩罚的时间一致性偏好管理者的最优策略相同.     

A Hyper-Erlang Jump-Diffusion Process and Applications in Finance

This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution. The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process. Finally, the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.     

Complete monotonicity of the probability of ruin and de Finetti’s dividend problem

This paper studies the complete monotonicity of the probability of ruinψin the the classical risk model and the classical risk model that is perturbed by a diffusion.As a byproduct,the authors give an alternative proof to a result on the optimal dividend problem due to LoefFen(2008).     

The compound binomial model with a constant dividend barrier and periodically paid dividends

Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends.A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived.Moreover,under a very relaxed condition,the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.     

Minimizing the Risk of Absolute Ruin Under a Diffusion Approximation Model with Reinsurance and Investment

This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions.The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario.Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy.The authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.     

Optimal investment problem for an insurer and a reinsurer

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors ?rst study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer: The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer's optimal investment strategies under the two cases.     

R&D企业最优技术投资与分红策略研究

本文研究了存在新技术项目时RD企业的最优技术投资与分红策略.假定企业流动资金变化由对偶风险模型描述,企业破产时存在清算价值,目标是最大化破产前的累计红利现值与清算价值现值之和.运用混合奇异控制-最优停时方法,当企业的每笔收益服从指数分布时本文得到RD企业的最优投资与分红策略及最优值函数的解析表达式.最后,我们分析了模型参数对企业最优投资与分红策略的影响,并用效用无偏差理论分析了新技术项目的价值.     

CEV模型下基于双曲绝对风险厌恶效用的最优投资策略

研究双曲绝对风险厌恶(HARA)型投资者在常弹性方差(CEV)模型下面临完全可对冲随机资金流时的最优动态资产配置问题.随机资金流可以视作一个外生负债,假定其服从带漂移的布朗运动.根据随机控制理论建立该问题的哈密顿-雅克比-贝尔曼(HJB)方程,通过猜测值函数的代数形式,将其化简为两个抛物型偏微分方程并分别求得显式解,从而得到最优投资策略.结果表明该非自融资组合的最优动态配置问题等价于初始财富为所有未来随机净资金流在风险中性测度下累积期望现值与初始稟赋之和的自融资组合的最优动态配置问题.投资策略由短视投资策略,动态对冲策略,静态对冲策略三部分组成.当对模型中参数取特殊值时,策略简化为已有文献的相应结果.最后分析了参数变化对于由随机资金流引起的额外投资需求的影响.     

奈特不确定下考虑逆向选择的最优动态契约设计

现实世界中不确定可以分成概率不确定和奈特（Knight）不确定.本文从奈特不确定框架研究连续时间下面临道德风险的委托-代理问题，试图分析低道德水平代理人逆向选择对高道德水平代理人延续价值和动态最优契约执行过程的影响.首先，基于非线性期望理论，利用G-布朗运动刻画契约项目盈利的动力学方程，进而定义了委托人和代理人的期望效用.其次，用带G-布朗运动驱动的随机微方程刻画了高道德水平代理人和低道德水平代理人价值过程.并且，利用次线性期望下的最优性原理，推导出高道德水平代理人预期效用值函数所满足的哈密尔顿-雅可比-贝尔曼（HJB）方程，在低道德水平代理人逆向选择下给出高道德水平代理人获得的最优报酬，同时得到低道德水平与高道德水平两类代理人最优努力水平的隐式表达式.最后，通过Matlab数值模拟，阐释了奈特不确定对委托人和不同类型代理人的策略影响.模拟分析结果表明，低道德水平代理人的逆向选择将会直接影响高道德水平代理人的契约支付，进而会影响契约有效性；而作为造成低道德水平代理人逆向选择的重要原因，奈特不确定也使得委托代理双方的决策更加谨慎.     

Optimal risk control policies for diffusion models with non-cheap proportional reinsurance and bankruptcy value

This paper considers the problem about optimization of proportional reinsurance in the setting of diffusion models. The authors take into account non-cheap proportional reinsurance and bankruptcy value simultaneously. The objective is to find the risk control policies which maximize the total discounted reserve and the bankruptcy value. Results show that, the optimal risk control policies and corresponding optimal return functions vary, depending both on the range of bankruptcy value and the relationship between the premium rate of insurance and that of reinsurance.     

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.     

不同支付条件银行授信约束折现流项目调度

支付条件对于项目现金流分布并进而对承包商的项目收益会产生重要影响.本文基于这一现实情况,研究不同支付条件下的银行授信额度约束折现流项目调度问题.作者首先综述该问题的研究现状;然后对所研究问题进行界定,进而构建项目调度优化模型;针对问题的NP-hard属性,设计模拟退火启发式算法;在随机生成的标准算例集合上,对算法的绩效进行对比测试及验证;最后用一个算例对研究进行说明,并分析项目收益对关键参数的敏感性,得到如下结论:项目净现值随银行授信额度和截止日期的增加而边际效应递减地上升,随支付比例的增加而线性单调上升,随折现率的增加以负指数形式下降.本文的研究可以为承包商安排项目进度并优化现金流量提供决策支持.     

易逝品随机生产库存模型动态定价、服务水平和生产控制策略

本文研究需求受价格和服务水平双重影响下的易逝品随机生产库存模型,探讨考虑外部随机扰动对库存变动影响下易逝品企业的最优联合动态定价、服务和生产策略,并基于随机最优控制理论,运用Hamilton-Jacobi-Bellman(HJB)方程对最优策略进行了求解.研究表明:最优动态价格、服务水平和生产速率是库存水平的线性反馈形式;外部随机扰动的大小对易逝品生产企业所获得的折现利润总期望会产生不同影响,在整个经营周期内外界不确定因素越大,易逝品生产企业所获得的折现利润总期望越小;价格敏感系数和服务敏感系数会影响易逝品企业生产、服务、价格策略.     

最优消费投资与破产保护

考虑一个面临经营性风险(非系统风险)的企业家, 在给定的债务及企业所得税率下, 如何通过消费平滑、实业投资、破产保护以及金融投资, 实现消费效用最大化的公司金融问题. 得到了非风险中性下企业资本价值的半闭式解及相应的最优经营策略和最优破产阈值. 对应经典的资本资产定价(CAPM)理论, 得出企业家的期望收益率、贝塔系数、系统风险溢价和非系统风险溢价(idiosyncratic risk premium). 不同于传统观点, 非系统风险溢价严格大于零. 这些结论和数值计算表明, 企业家的风险态度对企业资本价值、最优资本结构、实业投资策略、破产水平、非系统风险溢价、期望收益率等具有显著的影响.     

A multi-period pricing and inventory control model

<正> The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each other and their distributions depend on the product price.Pricing andordering decisions are made at the beginning of each period and all shortage are backlogged.Orderingcost is a convex function of the amount ordered.The objective is to find an inventory and pricing policymaximizing expected discounted profit over the finite horizon.The authors characterize the structure ofthe optimal combined pricing and inventory strategy for this model.Moreover,the authors demonstratehow the profit-to-go function,order up to level,reorder point and optimal price change with respectto state and time.     

排污约束下企业的投资与定价

考察了在政府对企业污染排放进行限制的条件下,当企业资本存在随机波动时企业如何进行动态投资和价值评估.运用随机动态最优控制方法,得到了企业价值的自由边界常微分方程以及相应的最优投资策略和治污策略.数值计算表明, 在企业资本规模较小时, 企业无排污支出,且排污约束对企业的投资和定价影响较弱, 而当企业资本规模较大时,企业必须支付一定的治污费用以降低自身的污染排放量; 同时,排污约束不仅显著降低了企业的总价值以及资本的平均和边际价值,还减小了企业的投资动机.     

超额配售选择权下的发行定价策略

以我国引入超额配售选择权的新股发行流程为基础,将发行定价策略分为热销策略和弱销策略进行分析和求解,并用具体算例进行比较.结果表明,承销商制定的发行价格直接关系到超额发售比例以及超额配售权的执行比例,选择最优发行定价策略时应根据具体的参数以及对上市初期价格的估计,通过比较2种策略的期望收益来决定.算例进一步说明,当上市初期价格的预期不是很高时,选择弱销策略最优;当预期上市初期价格过高时,承销商会选择热销策略.