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摘要翻译：
本文计算并讨论了指数过程的Esscher鞅变换，线性过程的Esscher鞅变换，最小鞅测度，保结构鞅测度，以及由Barndorff-Nielsen和Shephard引入的Ornstein-Uhlenbeck型随机波动模型的最小熵鞅测度。我们发现，在波动率和收益均有跳跃的有杠杆模型中，所有这些度量都是不同的；而在波动率仅有跳跃且收益连续的无杠杆模型中，几个度量是一致的，可以进行一些简化，结果更加明确。我们用文献中使用的参数例子来说明我们的结果。
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英文标题：
《On the Esscher transforms and other equivalent martingale measures for
Barndorff-Nielsen and Shephard stochastic volatility models with jumps》
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作者：
Friedrich Hubalek (Technical University of Vienna) Carlo Sgarra
(Technical University of Milan)
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最新提交年份：
2008
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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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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of Ornstein-Uhlenbeck type as introduced by Barndorff-Nielsen and Shephard. We show, that in the model with leverage, with jumps both in the volatility and in the returns, all those measures are different, whereas in the model without leverage, with jumps in the volatility only and a continuous return process, several measures coincide, some simplifications can be made and the results are more explicit. We illustrate our results with parametric examples used in the literature.
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PDF链接：
https://arxiv.org/pdf/0807.1227
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