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摘要翻译：
本文将混合指数跳跃扩散过程的首次通过时间限制在常边界。得到了首次通过次数分布、首次通过次数与下冲（过冲）联合分布的拉普拉斯变换的显式解。作为应用，我们给出了具有双边跳跃的盈余过程的Gerber-Shiu函数的显式表达式，给出了常用的路径依赖期权如回望期权和障碍期权的Laplace变换的解析解，并给出了具有跳跃的结构信用风险模型下零息债券价格的闭式表达式。
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英文标题：
《The first passage time problem for mixed-exponential jump processes with
applications in insurance and finance》
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作者：
Chuancun Yin, Yuzhen Wen, Zhaojun Zong, Ying Shen
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最新提交年份：
2014
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.
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PDF链接：
https://arxiv.org/pdf/1302.6762
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