论文标题
最小的kullback-leibler差异，用于受限的lévy-itô流程
Minimal Kullback-Leibler Divergence for Constrained Lévy-Itô Processes
论文作者
论文摘要
考虑到由p-brownian动作和泊松随机度量驱动的N维随机过程X，我们寻求概率度量Q，而P的相对熵最少，因此某些终端成本和运行成本的Q期望受到限制。我们证明了最佳概率度量的存在和独特性，得出了量度变化的明确形式，并表征了最佳度量下的最佳漂移和补偿器调整。我们为价值风险（分位数）约束提供了一个分析解决方案，讨论如何扰动布朗运动以具有任意方差，并表明将固定的度量作为最佳度量的限制情况。在风险管理设置中说明了结果 - 包括在最佳度量下模拟的算法 - 代理商试图回答问题：通过危险的扰动以及在参考过程中遇到的平均时间诱导了哪些动态？
Given an n-dimensional stochastic process X driven by P-Brownian motions and Poisson random measures, we seek the probability measure Q, with minimal relative entropy to P, such that the Q-expectations of some terminal and running costs are constrained. We prove existence and uniqueness of the optimal probability measure, derive the explicit form of the measure change, and characterise the optimal drift and compensator adjustments under the optimal measure. We provide an analytical solution for Value-at-Risk (quantile) constraints, discuss how to perturb a Brownian motion to have arbitrary variance, and show that pinned measures arise as a limiting case of optimal measures. The results are illustrated in a risk management setting -- including an algorithm to simulate under the optimal measure -- where an agent seeks to answer the question: what dynamics are induced by a perturbation of the Value-at-Risk and the average time spent below a barrier on the reference process?
