论文标题
有效评估稳定的Lévy过程功能的期望及其极值
Efficient evaluation of expectations of functions of a stable Lévy process and its extremum
论文作者
论文摘要
得出了稳定的lévy流程$ x $及其最高$ \ bar x $功能期望的积分表示。作为示例，累计概率分布函数（CPDF）为$ x_t，\ barx_t $，$ x_t $和$ \ barx_t $的联合CPDF，以及$（\ be x_t- \ barx_t）_++$，$ \ $ \ be> 1 $的期望（\ be x_t- \ barx_t）_ $ he> 1 $，以及有效的cpd。最有效的数值方法使用保形加速技术和简化的梯形规则。
Integral representations for expectations of functions of a stable Lévy process $X$ and its supremum $\bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, \barX_T$, the joint cpdf of $X_T$ and $\barX_T$, and the expectation of $(\be X_T-\barX_T)_+$, $\be>1$, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule.
