摘要翻译:
我们在R_+上的R_d值C_adl_ag函数的空间D(R_+,R_d)上建立了一系列经验测度,以逼近暂态R_d值Markov和Feller过程(X_t)的规律。我们得到了该序列收敛性的一些推广结果。然后,在Lyapunov型稳定性假设下,我们将它们应用于BrownianDifferences和L\'evy驱动SDE的解。作为这一工作的一个数值应用,我们证明了这一过程给出了随机波动率模型中期权定价的一种有效方法。
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英文标题:
《Approximation of the distribution of a stationary Markov process with
application to option pricing》
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作者:
Gilles Pag\`es (PMA, LSProba), Fabien Panloup (PMA)
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最新提交年份:
2009
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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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一级分类:Quantitative Finance 数量金融学
二级分类:Pricing of Securities 证券定价
分类描述:Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要:
We build a sequence of empirical measures on the space D(R_+,R^d) ofR^d-valued c\`adl\`ag functions on R_+ in order to approximate the law of astationary R^d-valued Markov and Feller process (X_t). We obtain some generalresults of convergence of this sequence. Then, we apply them to Browniandiffusions and solutions to L\'evy driven SDE's under some Lyapunov-typestability assumptions. As a numerical application of this work, we show thatthis procedure gives an efficient way of option pricing in stochasticvolatility models.
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PDF链接:
https://arxiv.org/pdf/0704.0335