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摘要翻译：
我们考虑一个Markov过程$x$，它是由L\'{e}vy过程$z$和独立的Wiener过程$w$驱动的随机微分方程的解。在一定的正则性条件下，包括扩散分量和跳跃分量的非简并性，以及在原点的任意邻域外的L{e}vy密度$z$的光滑性，我们得到了尾分布和跃迁密度$x$的一个小时间二阶多项式展开式。我们的证明方法结合了一种新的用于推导L{e}vy过程模拟小时间展开式的正则化技术和基于Malliavin微积分理论、SDEs的微分同态流和时间可逆性的具有小跳跃的跳跃-扩散过程的一些新的尾和密度估计。作为应用，本文还导出了局部跳扩散模型下短期货币外期权价格的先导项。
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英文标题：
《Small-time expansions for local jump-diffusion models with infinite jump
activity》
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作者：
Jos\'e E. Figueroa-L\'opez, Yankeng Luo, Cheng Ouyang
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最新提交年份：
2014
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分类信息：
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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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：
We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a L\'{e}vy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the L\'{e}vy density of $Z$ outside any neighborhood of the origin, we obtain a small-time second-order polynomial expansion for the tail distribution and the transition density of the process $X$. Our method of proof combines a recent regularizing technique for deriving the analog small-time expansions for a L\'{e}vy process with some new tail and density estimates for jump-diffusion processes with small jumps based on the theory of Malliavin calculus, flow of diffeomorphisms for SDEs, and time-reversibility. As an application, the leading term for out-of-the-money option prices in short maturity under a local jump-diffusion model is also derived.
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PDF链接：
https://arxiv.org/pdf/1108.3386
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