论文标题
γ驱动随机微分方程的非参数贝叶斯波动率估计
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
论文作者
论文摘要
我们研究了一种非参数贝叶斯方法，用于估计由伽马过程驱动的随机微分方程的波动率函数。挥发率函数被建模为先验函数，为分段常数，我们在其值上指定了伽玛的先验。这导致了通过MCMC程序进行后验推断的直接过程。我们根据未知波动率函数的规律性，给出了贝叶斯估计值的理论性能保证（后部的收缩率）。我们说明了合成和真实数据示例的方法。
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward procedure for posterior inference via an MCMC procedure. We give theoretical performance guarantees (contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.
