Efficient Evaluation of Expectations of Functions of a Stable Levy Process and Its Extremum

Download or read book Efficient Evaluation of Expectations of Functions of a Stable Levy Process and Its Extremum written by Svetlana Boyarchenko and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral representations for expectations of functions of a stable L 'evy 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.