论文标题
Gerber-Shiu理论用于政权转换环境中的离散风险过程
Gerber-Shiu Theory for Discrete Risk Processes in a Regime Switching Environment
论文作者
论文摘要
在本文中，我们开发了马尔可夫（政权切换）环境中经典和双离散风险过程的Gerber-Shiu理论。特别是，通过表达Gerber-shiu功能，以向上（向下）无离散时间和离散空间马尔可夫添加剂过程（MAP）的潜在度量来表示Gerber-shiu功能的封闭形式表达式，以所谓的（离散）$ \ boldsymbol {w} _ $ s $ s $ s $ al s $ bolds n dyd dyps y bolds y bold as y bold bold bold bold lass y bold bold bold bold bold bold bold bold lass n bold bold。在Arxiv中引入：2008.06697。我们表明，离散量表矩阵允许采用统一的方法来识别Gerber-Shiu功能以及相关的恒定股息屏障问题的价值函数。
In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an upward (downward) skip-free discrete-time and discrete-space Markov Additive Process (MAP), we derive closed form expressions for the Gerber-Shiu function in terms of the so-called (discrete) $\boldsymbol{W}_v$ and $\boldsymbol{Z}_v$ scale matrices, which were introduced in arXiv:2008.06697. We show that the discrete scale matrices allow for a unified approach for identifying the Gerber-Shiu function as well as the value function of the associated constant dividend barrier problems.
