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This paper assumes that company's asset process follows a non-linear model, which reflects the relationship between the operation costs and the size business. Suppose that the company can control the asset process by changing the size of business, paying dividends and raising money dynamically. Meanwhile, it bears both fixed and proportional transaction costs during the control processes. Under the objective of maximizing the company's value, we obtain the explicit solutions of optimal strategies and value function by using the optimal control method. The results illustrate that the optimal strategies depend on the parameters of the model. The company should expand the business scale with the increasing of asset. Dividends should be paid out according to the impulse control strategy. Financing is profitable to avoid bankruptcy if and only if the transaction costs are relatively low.     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

含交易费用的投资组合问题的新模型及其求解途径

本文提出了证券投资组合的一个新模型.该模型综合考虑了证券的收益率、证券分红和证券价格的关系,并将证券分红和证券价格作为系统的随机参数处理,建立了证券投资组合的随机规划模型.利用机会约束规划方法,我们研究了将所建立的随机规划模型转化为普通光滑优化问题求解的方法,得到了该类问题求解的有效途径.     

阈值分红策略下带常利率的对偶风险模型

研究了常利率下基于对偶复合泊松模型带阈值的分红策略,给出了公司在破产时累积红利期望现值函数的两个积分-微分方程,分情况讨论了收益服从指数分布时的显示表达式,以及服从一般分布时的拉普拉斯变换表达式.     

不同风险度量约束下带有红利的投资组合模型研究

对现有的在风险度量约束下的投资组合模型进行了推广.建立了带有红利情形的随机股票市场模型,给出了投资组合关于这些风险度量约束下的最优化结果.     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein-Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein-Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.     

常利息力影响下跳扩散模型的分红问题

本文中用常值利率驱动下的经典跳扩散模型模拟保险公司的盈余过程,研究了该模型在带壁分红策略下的若干问题.首先得出破产前分红折现的高阶矩所满足的积分微分方程,并在指数分布的情况下借助合流超几何函数给出了方程的显式解.其次关于破产前聚合分红得到了一些令人满意的结果,这些结果甚至对一般的分布都成立,另外讨论了分红流的次数和额度.最后研究了指数分布时破产赤字折现期望问题.本文的部分结论深化了精算学中一些已有研究成果.     

The compound Poisson risk model with dependence under a multi-layer dividend strategy

In this paper, a compound Poisson risk model with time-dependent claims is studied under a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber-Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.     

Optimal dividend strategies in discrete risk model with capital injections

In this paper we consider a doubly discrete model used in Dickson and Waters (biASTIN Bulletin 1991; 21 :199–221) to approximate the Cramér–Lundberg model. The company controls the amount of dividends paid out to the shareholders as well as the capital injections which make the company never ruin in order to maximize the cumulative expected discounted dividends minus the penalized discounted capital injections. We show that the optimal value function is the unique solution of a discrete Hamilton–Jacobi–Bellman equation by contraction mapping principle. Moreover, with capital injection, we reduce the optimal dividend strategy from band strategy in the discrete classical risk model without external capital injection into barrier strategy , which is consistent with the result in continuous time. We also give the equivalent condition when the optimal dividend barrier is equal to 0. Although there is no explicit solution to the value function and the optimal dividend barrier, we obtain the optimal dividend barrier and the approximating solution of the value function by Bellman's recursive algorithm. From the numerical calculations, we obtain some relevant economical insights. Copyright © 2010 John Wiley & Sons, Ltd.     

Dividend Maximization when Cash Reserves Follow a Jump-diffusion Process

This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman （HJB） equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.