多维仿射扩散中指数矩的长期和爆破行为
Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions
摘要：
本文考虑具有连续样本路径的多维仿射过程。通过分析Riccati系统，利用变换公式将Riccati系统与仿射过程联系起来，充分刻画了给定过程的指数矩在任意时刻不爆炸或在给定时刻爆炸的指数区域.在这两种情况下，我们还计算了指数矩的长期增长率和爆炸率。这些结果提供了一个手柄，研究模型中的隐含波动率渐近股票价格的回报率描述的仿射过程的指数矩没有一个明确的公式。
英文摘要：
This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.
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