英文标题：
《Feynman-Kac formula for L\\\'evy processes with discontinuous killing rate》
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作者：
Kathrin Glau
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最新提交年份：
2015
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英文摘要：
  The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in L\\\'evy models by solving partial integro differential equations have been developed. In order to provide a solid mathematical foundation for these methods, we derive a Feynman-Kac representation of variational solutions to partial integro differential equations that characterize conditional expectations of functionals of killed time-inhomogeneous L\\\'evy processes. We allow for a wide range of underlying stochastic processes, comprising processes with Brownian part, and a broad class of pure jump processes such as generalized hyperbolic, multivariate normal inverse Gaussian, tempered stable, and $\\alpha$-semi stable L\\\'evy processes. By virtue of our mild regularity assumptions as to the killing rate and the initial condition of the partial differential equation, our results provide a rigorous basis for numerous applications, not only in financial mathematics but also in probability theory and relativistic quantum mechanics.
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中文摘要：
将数学金融和数值分析的最新技术有效地结合起来的挑战促使研究人员开发出快速确定的期权定价方法。因此，通过求解偏积分-微分方程，开发了在列维模型中计算期权价格的高效算法。为了为这些方法提供坚实的数学基础，我们推导了偏积分-微分方程变分解的Feynman-Kac表示，该方程描述了非齐次LSevy过程泛函的条件期望。我们考虑了广泛的潜在随机过程，包括布朗部分的过程，以及广泛的纯跳跃过程，如广义双曲、多元正态逆高斯、调和稳定和$\\alpha$-半稳定的LSevy过程。由于我们对杀伤率和偏微分方程初始条件的温和正则性假设，我们的结果为金融数学、概率论和相对论量子力学的许多应用提供了严格的基础。
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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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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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