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 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 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.     

Optimal Reinsurance Under Distortion Risk Measures and Expected Value Premium Principle for Reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer’s risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer’s optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.     

考虑违约风险的兼顾保险公司与再保险公司利益的最优投资与再保险问题研究

本文主要研究了考虑违约风险的兼顾保险公司与再保险公司共同利益的最优投资与再保险问题.假设索赔过程由带漂移的几何布朗运动描述,保险公司可以投资于一无风险资产、一支股票和一可违约债券,再保险公司可以投资于一无风险资产和一支股票.以两家公司终端财富的期望指数效用乘积最大为目标,采用随机控制理论建立优化问题对应的HJB方程,进而分别得到违约前和违约后的最优策略和价值函数.最后本文分析了各模型参数对最优投资和再保险策略的影响,并给出相应的经济解释.     

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.     

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.     

基于偿付能力的最优再保险策略

采用最大索赔再保费定价原则,结合VaR、CTE、TV三种风险测度方法,通过研究最小化偿付不足风险的概率、期望损失以及均方期望超额损失等再保险问题,得到相应的最优再保险策略,并结合案例对各种最优策略进行静态分析.研究发现,当偿付能力基于VaR或者CTE时,最优的再保险策略是去尾停止损失再保险,这说明原保险公司此时应该更注重对中等巨额损失的保障,而没有动力去保障极值损失;当偿付能力基于TV时,最优策略是带限额的停止损失再保险,此时,保险公司为了保证经营的稳定性,势必会将一部分极值损失分保.     

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.     

风险调整资本收益率下的最优再保险策略

引入金融行业中用在风险管理和绩效评估等方面的指标——风险调整资本收益率,构建了基于该指标的再保险策略风险模型.对于常用的成数再保险和停止损失再保险,通过分析得出了使得保险人风险调整资本收益率最大化的自留风险比率和自留风险额度.同时发现:对于成数再保险,保险人可以通过自留所有风险来获得最大的风险调整资本收益率;而对于停止损失再保险,如果保险偿付能力监管的资本要求足够严格,保险人存在一个最优的自留风险额度.在此额度下,保险人能够获得比保留所有风险更大的风险调整资本收益率.     

资金约束下订单农业供应链中的农户最优决策

考虑农户受资金约束以及产出随机性,构建由单个农户和单个公司组成的订单农业供应链决策模型.在对比分析无资金约束下农户最优决策基础上,分别研究资金约束下不同情形(情形1:农户不存在破产风险;情形2:农户存在破产风险)中的农户最优决策,并得了到资金约束下农户最优决策的选择策略.研究表明:1)价格弹性系数可显著影响资金约束下的农户最优期望利润.2)调节贷款利率,可使资金约束下情形2中的农户最优生产投入量达到无资金约束下的最优水平.3)丰收年产出因子与贷款利率是影响农户最优决策选择的关键因素:①当丰收年产出因子低时,农户将选择情形1的最优决策,且与贷款利率无关;②当丰收年产出因子高时,低(高)的贷款利率会使农户选择情形1(情形2)的最优决策.     

S型效用下比例再保险的最优投资策略

本文引入了行为金融学中的损失厌恶概念,研究考虑损失厌恶时保险公司的最优投资再保险问题.在损失厌恶下,保险公司面对盈利时是风险厌恶者,而遭受损失时转为风险追求者,因此本文采用S型效用函数,并以终端财富的效用最大化为目标求解保险公司的最优策略.假定保险公司的盈余过程服从经典的Cramer-Lundberg模型,可将资产投资于一种无风险资产和一种服从几何布朗运动的风险资产,且可以通过向再保险公司购买比例再保险来分散风险、稳定经营.通过构造鞅过程,运用鞅方法和拉格朗日对偶法求解出最优策略与最优财富.最后进行数值分析,更加直观地解释了各经济参数对财富值和投资策略的影响.     

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.     

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．     

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.     

大型项目融资风险动态管理方法

首先给出了针对破产风险、收益风险以及资本结构风险的大型项目风险管理方法体系——融资风险指标监控法、NPV和PaR指标监控法以及B指标监控法。其次,在项目随机变量的预测方面,引入一个有偏的损失函数来解决同样的预测失误量,即预测错误给投资者带来的损害绝对值要大于预测正确给投资者带来的收益绝对值这一问题。最后,用一个水厂案例进行了实例研究。     

投资连结产品的再保险策略

对趸缴保费和分期缴纳保费两种情况，在投资基金服从对数正态分布的假定下，研究投资连结产品在经营期内每年的最优比例再保险和超额损失再保险策略，所得结论对保险人做此决策具有直接的指导作用。     

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.     

带有通胀风险的退休后期最优投资管理

考虑通货膨胀的影响,研究了一个确定缴费养老计划退休后期最优投资决策问题.自退休时刻开始,退休者定期从账户里抽取一定的金额维持日常支出,然后将剩余的财富投资于一个无风险资产、一个股票指数和一个通胀指数债券,直到强制购买年金的时刻.为保障退休后的正常生活,退休者在每个时刻设定投资的目标值,采取二次效用函数衡量投资财富水平和目标值的差距,并选择最优的投资策略以最小化平均累计差距.运用动态规划和随机控制方法,得到了没有上方惩罚的目标值、最优投资策略、最优值函数、破产概率以及终端财富与目标值差距的分布函数等指标的显式表达式.运用数学分析和数值分析手段,得到了每个时刻目标值的性质,分析了终端目标值和消费金额对破产概率的影响,研究了物价指数的瞬间变化率和波动率对财富值与目标值的差距、各时刻财富均值以及破产概率的影响.     

随机巨灾索赔相依风险模型的动态最优再保险

在索赔风险时变、相依条件下,建立随机巨灾的可调态再保险模型.在指明超额赔款再保险为最优分保形式的基础上,讨论并发现目标函数随自留巨灾风险水平的增大,在任意相依结构下均先减后增的变化定理,从而获得了自留向量的一般性显式表达式.根据巨灾风险的特征,还在一类特定的相依结构下,以自留风险的期望效用和方差为优化目标,对自留向量进行了更为明确的表示并给出具体示例.结果表明,随着巨灾风险相依强度的上升,分保的满意度降低,经营稳定性减弱,对保险公司的负面影响很大.此时,为实现客观风险下的分保目标最优,常规风险的自留水平应随之增大,体现了动态再保险的优越性.