更新风险模型等价鞅测度的刻画及其在保费计算中的应用
A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles
摘要：
推广了Delbaen和Haezendonck的早期工作，对于给定的复合更新过程$S$在概率测度$P$下，我们刻画了$P$域上的所有概率测度$Q$，使得$Q$和$P$是渐进等价的，并且$S$在$Q$下仍然是复合更新过程。因此，我们证明了任何复合更新过程可以转换成一个复合泊松过程通过改变措施，我们展示了这种方法是如何与保费计算原则。
英文摘要：
Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process $S$ under a probability measure $P$ we characterize all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ remains a compound renewal process under $Q$. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
