论文标题
在最后一个零过程中，申请公司破产
On the last zero process with an application in corporate bankruptcy
论文作者
论文摘要
对于频谱负Lévy流程$ x $，请考虑$ g_t $，上次$ x $低于时间$ t \ geq 0 $。我们使用一种扰动方法来用于lévy进程来为三维过程$ \ {（g_t，t，x_t），t \ geq 0 \} $及其无限发电机得出ITô公式。此外，使用$ u_t：= t-g_t $，当前正偏移的长度，我们得出了一个通用公式，使我们能够计算$（u，x）= \ {（u_t，x_t），t \ geq 0 \} $的整个路径的函数，以$ x $ x $的正面和负面偏移。作为推论，我们发现$（U _ {\ MathBf {e} _Q}，X _ {\ MathBf {E} _Q}）$的联合拉普拉斯变换，其中$ \ Mathbf {e} _q $是独立的指定时间，Q-Potential的Q-Potential量和Q-Potential量量；此外，使用上面提到的结果，我们找到了一种解决方案，该解决方案取决于$（u，x）$的一般最佳停止问题，并在公司破产中申请了。最后，我们建立了$ g _ {\ infty} $的最佳预测与根据Baurdoux和Pedraza（2024）的最佳预测与最佳停止问题之间的联系。
For a spectrally negative Lévy process $X$, consider $g_t$, the last time $X$ is below the level zero before time $t\geq 0$. We use a perturbation method for Lévy processes to derive an Itô formula for the three-dimensional process $\{(g_t,t, X_t), t\geq 0 \}$ and its infinitesimal generator. Moreover, with $U_t:=t-g_t$, the length of a current positive excursion, we derive a general formula that allows us to calculate a functional of the whole path of $ (U, X)=\{(U_t, X_t),t\geq 0\}$ in terms of the positive and negative excursions of the process $X$. As a corollary, we find the joint Laplace transform of $(U_{\mathbf{e}_q}, X_{\mathbf{e}_q})$, where $\mathbf{e}_q$ is an independent exponential time, and the q-potential measure of the process $(U, X)$. Furthermore, using the results mentioned above, we find a solution to a general optimal stopping problem depending on $(U, X)$ with an application in corporate bankruptcy. Lastly, we establish a link between the optimal prediction of $g_{\infty}$ and optimal stopping problems in terms of $(U, X)$ as per Baurdoux and Pedraza (2024).
