常数红利边界下的一类马氏风险模型

本文研究了常数红利边界下一类马氏风险模型的红利派发矩,破产前所有红利的分布等相关问题.利用更新方法,给出了该模型破产前红利折现的期望满足的微分-积分方程,得到破产前所有红利的分布.通过构造特殊的初始条件,得到了相关的方程组解,推广了文献[3]的结果.     

保费和索赔到达率与余额相依的最优有界分红率问题

研究保费和索赔到达率与余额相依的最优有界分红问题,目标是最大化破产前的累积期望折现分红。首先,给出一个策略是平稳马氏策略的充分必要条件,运用测度值生成元的理论得到测度值动态规划方程（DPE）,并且给出了验证定理的证明。最后,讨论了测度值DPE和相应拟变分不等式（QVI）之间的关系,并且证明了最优分红策略为具有波段结构的平稳马氏策略。     

A Markov-modulated model for stocks paying discrete dividends

We extend the model in [Korn, R., Rogers, L.C.G., 2005. Stock paying discrete dividends: modelling and option pricing. Journal of Derivatives 13, 44–49] for (discrete) dividend processes to incorporate the dependence of assets on the market mode or the state of the economy, where the latter is modeled by a hidden finite-state Markov chain. We then derive the resulting dynamics of the stock price and various option-pricing formulae. It turns out that the stock price jumps not only at the time of the dividend payment, but also when the underlying Markov chain jumps.     

Smoothness of certain functions in two kinds of risk models with a barrier dividend strategy

In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy.Mainly using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk model.Using the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk model.Intego-differential equations satisfied by them are derived.     

Classical Risk Model with Threshold Dividend Strategy

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.     

具有常红利边界的复合马尔可夫二项模型

主要讨论复合马尔可夫二项模型.在模型中引进一个常数红利边界策略,得到了Gerber-Shiu罚金函数所满足的线性方程组,且证明该方程组存在唯一解.最后,作为罚金函数的一些应用实例给出了一些具体风险量的计算公式.     

A note on moments of dividends

We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative Lévy risk model that was obtained in Renaud and Zhou (2007, [4]) and in Kyprianou and Palmowski (2007, [3]) and extend the result to stationary Markov processes that are skip-free upwards.     

Optimal Reinsurance and Dividend Strategies Under the Markov-Modulated Insurance Risk Model

In this article, we consider the optimal reinsurance and dividend strategy for an insurer. We model the surplus process of the insurer by the classical compound Poisson risk model modulated by an observable continuous-time Markov chain. The object of the insurer is to select the reinsurance and dividend strategy that maximizes the expected total discounted dividend payments until ruin. We give the definition of viscosity solution in the presence of regime switching. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman equation and a verification theorem is also obtained.     

Classical and singular stochastic control for the optimal dividend policy when there is regime switching

Motivated by economic and empirical arguments, we consider a company whose cash surplus is affected by macroeconomic conditions. Specifically, we model the cash surplus as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study two different cases: bounded dividend rates and unbounded dividend rates. These cases generate, respectively, problems of classical stochastic control with regime switching and singular stochastic control with regime switching. We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. We prove that the optimal dividend policy depends strongly on macroeconomic conditions.     

Asymptotically optimal dividend policy for regime-switching compound Poisson models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.