一类保费批量到达的双险种风险模型

本文研究了一类保费与索赔均为批量到达的双险种破产模型,在特定的分布下导出了调节系数方程,得到了初始资本为u的破产概率的上界并与非批量到达的模型的破产上界进行了比较。     

广义复合二项风险模型下的破产概率

将复合二项风险模型的保费收入推广为在单位时间内收取的保单数服从强度为α的poisson分布，利用鞅方法得出了其破产概率的一般公式及满足Lundberg不等式。     

变破产下限风险模型的破产概率

近年来,很多文献对经典风险模型作了研究,并得出许多有用的结论。一般文献都是假定保险公司的破产下限为零,但在实际的保险实务中,当保险公司的盈余低于某一限度时,保险公司就要调整政策或宣布破产。本文研究了经典风险模型在假定变破产下限下的破产概率,得出了破产概率所满足的不等式,而且研究了当破产下限f(t)为某些特殊函数时,破产概率所满足的不等式或破产概率的具体表达式。最后本文给出了在推广后的风险模型中变破产下限破产概率所满足的不等式。     

基于跳扩散过程的Omega模型

文章通过在Omega模型中加入布朗运动扰动项,提出了一种跳扩散Omega破产模型.在索赔额为指数分布的情形下,给出了破产率函数是常数时的破产概率函数表达式.文章进一步研究了破产概率和盈余过程的“负占有时”之间的关系,并给出了破产概率函数的第二种推导过程.最后通过两个数值试验,将我们的模型与Albreeher和Lautscham (2013)的Omega模型的破产概率进行了比较分析.     

马氏风险过程

研究了一般马氏风险过程,它是经典风险过程的拓广．具有大额索赔的风险过程用此马氏风险模型来描述是适合的．在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数．主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界．     

一类推广负风险和模型的破产概率

本文研究了带干扰的两险种负风险和模型的破产问题.利用无穷小方法,给出了该风险模型破产概率所满足的微分-积分方程,并推导出破产概率满足的Lundberg型不等式.最后指出了当索赔服从负指数分布时破产概率的上界,推广了经典风险模型的结果.     

具有相关索赔风险模型的破产概率

本文考虑了具有两类索赔的风险模型,这两类索赔的计数过程是相关的Poisson过程和Erlang过程.通过Laplace变换方法,得到了该风险模型在索赔额为任意分布情形下破产概率的计算公式,并在索赔额为指数分布的情形下,得到了破产概率的精确表达式.     

一类推广的双险种复合Poisson风险模型的破产概率

本文研究了一类索赔计数过程相关的双险种Poisson风险模型.利用模型转化首先将该复杂模型转化为经典的风险模型,获得该模型破产概率所满足的积分方程,Lundberg上界表达式,及Cramér-Lundberg渐近估计式.当个体索赔具有指数分布时,推得了破产概率所满足的方程,并给出了具体的数值计算的实例.     

复合Poisson-geometric风险模型下第n次索赔时的破产概率研究

在复合Poisson-geometric风险模型下,通过构造一个特殊的Gerber-Shiu函数,推导出此风险模型下Gerber-Shiu函数满足的更新方程,破产时刻和直到破产时的索赔次数的联合密度函数,得到了第n次索赔时的破产概率的数学表达式．     

索赔为一般到达的保险风险模型

本文应用作者们提出和建立的Markov骨架过程方法，研究了索赔为一般到达的保险风险模型，得到了破产时间分布以及破产时间与破产时刻前后资产盈科的联合分布，由此可计算出人们关心的一些重要指标。     

Multi-period portfolio optimization for asset–liability management with bankrupt control

In this paper, we investigate a multi-period portfolio optimization problem for asset–liability management of an investor who intends to control the probability of bankruptcy before reaching the end of an investment horizon. We formulate the problem as a generalized mean–variance model that incorporates bankrupt control over intermediate periods. Based on the Lagrangian multiplier method, the embedding technique, the dynamic programming approach and the Lagrangian duality theory, we propose a method to solve the model. A numerical example is given to demonstrate our method and show the impact of bankrupt control and market parameters on the optimal portfolio strategy.     

一类比例保险模型的破产概率问题

研究了比例再保险的破产概率问题,推广了Gramer-Lundberg经典模型的有关结果,并证明了基于比例模型合保问题最低保费的一个结果。     

Mean-CVaR模型下的资产组合和破产风险控制

为了克服尾部风险测度CVaR模型本身的不足，并且给“如何实现资产组合的破产风险与期望利润的最优配置”问题提供一个更加符合现实的答案，本文在CVaR模型基础上，通过把风险资本的来源内生于资本禀赋以及把风险资本的机会成本引入利润函数的方式提出了线性Mean—CVaR模型。同时，本文通过对“上证50”成分股进行选择的实证分析给出了由线形Mean—CVaR模型得到的更加合理的资产组合与资本储备。     

数据包络分析在信用评估中的应用

提出了一种基于拒绝案例集的数据包络分析模型和边界为分段线性分离超平面的分类方法，探讨了在只掌握单方面信息(信用差的单位)的情况下，如何对新单位进行信用评估的问题，并给出了评价决策单元信用状况的具体方法，应用实例表明所提出的模型和方法是可行的。     

Optimal control of a big financial company with debt liability under bankrupt probability constraints

This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business policies from an available set of control policies with different expected profits and risks, controls the business policy and dividend payout process to maximize the expected present value of the dividends until the time of bankruptcy. However, if the dividend payout barrier is too low to be acceptable, it may result in the company’s bankruptcy soon. In order to protect the shareholders’ profits, the managements of the company impose a reasonable and normal constraint on their dividend strategy, that is, the bankrupt probability associated with the optimal dividend payout barrier should be smaller than a given risk level within a fixed time horizon. This paper aims at working out the optimal control policy as well as optimal return function for the company under bankrupt probability constraint by stochastic analysis, partial differential equation and variational inequality approach. Moreover, we establish a riskbased capital standard to ensure the capital requirement can cover the total given risk by numerical analysis, and give reasonable economic interpretation for the results.     

Dynamic optimal portfolio with maximum absolute deviation model

In this paper, a new dynamic portfolio selection model is established. Different from original consideration that risk is defined as the variance of terminal wealth, the total risk is defined as the average of the sum of maximum absolute deviation of all assets in all periods. At the same time, noticing that the risk during the period is so high that the investor may go bankrupt, a maximum risk level is given to control risk in every period. By introducing an auxiliary problem, the optimal strategy is deduced via the dynamic programming method.     

Bankruptcy theory development and classification via genetic programming

Bankruptcy is a highly significant worldwide problem with high social costs. Traditional bankruptcy risk models have been criticized for falling short with respect to bankruptcy theory building due to either modeling assumptions or model complexity.Genetic programming minimizes the amount of a priori structure that is associated with traditional functional forms and statistical selection procedures, but still produces easily understandable and implementable models. Genetic programming was used to analyze 28 potential bankruptcy variables found to be significant in multiple prior research studies, including 10 fraud risk factors. Data was taken from a sample of 422 bankrupt and non-bankrupt Norwegian companies for the period 1993–1998. Six variables were determined to be significant.A genetic programming model was developed for the six variables from an expanded sample of 1136 bankrupt and non-bankrupt Norwegian companies. The model was 81% accurate on a validation sample, slightly better than prior genetic programming research on US public companies, and statistically significantly better than the 77% accuracy of a traditional logit model developed using the same variables and data. The most significant variable in the final model was the prior auditor opinion, thus validating the information value of the auditor’s report. The model provides insight into the complex interaction of bankruptcy related factors, especially the effect of company size. The results suggest that accounting information, including the auditor’s evaluation of it, is more important for larger than smaller firms. It also suggests that for small firms the most important information is liquidity and non-accounting information.The genetic programming model relationships developed in this study also support prior bankruptcy research, including the finding that company size decreases bankruptcy risk when profits are positive. It also confirms that very high profit levels are associated with increased bankruptcy risk even for large companies an association that may be reflecting the potential for management to be “Cooking the Books”.     

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 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.     

Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences

In this paper, we consider an optimal dividend-financing problem for a company whose capital reserve is described by the dual of classical risk model. We assume that the manager of the company has time-inconsistent preferences, which are described by a quasi-hyperbolic discount function, and that financing is permitted to prevent the company from going bankrupt. The manager’s objective is to maximize the expected cumulative dividend payments minus financing costs. We solve the optimization problems for a naive manager and a sophisticated manager, and obtain explicit solutions for both managers. Our results show that the manager with time-inconsistent preferences tends to pay out dividends earlier. We also present some economic implications and sensitivity analysis for our results.