论文标题
CBI时间改变的莱维过程
CBI-time-changed Lévy processes
论文作者
论文摘要
我们介绍并研究了CBI时代变化的Lévy过程（CBITCL）的类别，该过程是通过随着时间的变化而与移民（CBI）进行综合的连续分支过程相对于综合连续分支过程获得的。我们将CBITCL过程表征为对某个随机积分方程的解决方案，并将其与仿射随机波动过程相关联。我们对CBITCL过程的指数力矩爆炸时间进行完整分析并研究其渐近行为。此外，我们表明CBITCL过程相对于一类合适的等效度量变化是稳定的。如某些示例所示，CBITCL过程是灵活的和可拖动的过程，具有巨大的财务应用潜力。
We introduce and study the class of CBI-time-changed Lévy processes (CBITCL), obtained by time-changing a Lévy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral equation and relate them to affine stochastic volatility processes. We provide a complete analysis of the time of explosion of exponential moments of CBITCL processes and study their asymptotic behavior. In addition, we show that CBITCL processes are stable with respect to a suitable class of equivalent changes of measure. As illustrated by some examples, CBITCL processes are flexible and tractable processes with a significant potential for applications in finance.
