In this paper, we investigate the reflected CIR process with two-sided jumps to capture the jump behavior and its non-negativeness. Applying the method of (complex) contour integrals, the closed-form solution to the joint Laplace transform of the first passage time crossing a lower level and the corresponding undershoot is derived. We further extend our arguments to the exit problem from a finite interval and obtain joint Laplace transforms. Our results are expressed in terms of the real and imaginary parts of complex functions by complex matrix. Numerical results are included.

中文翻译：

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具有双向跳跃的反射CIR流程的退出时间，下冲和上冲

在本文中，我们研究了具有双向跳跃的反射CIR过程，以捕获跳跃行为及其非负性。应用（复数）轮廓积分的方法，得出第一穿越时间越过较低水平的联合拉普拉斯变换的闭式解，并得出相应的下冲。我们进一步从有限的区间扩展对出口问题的论据，并获得联合拉普拉斯变换。我们的结果用复数矩阵表示为复数函数的实部和虚部。包括数值结果。