Efficient evaluation of expectations of functions of a stable L\'evy process and its extremum

Svetlana Boyarchenko; Sergei Levendorskiĭ

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arXiv · 2209.12349

Efficient evaluation of expectations of functions of a stable L\'evy process and its extremum

Svetlana Boyarchenko·Sergei Levendorskiĭ

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Abstract

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.

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Svetlana Boyarchenko, Sergei Levendorskiĭ. 2022-09-25. Efficient evaluation of expectations of functions of a stable L\'evy process and its extremum. https://arxiv.org/abs/2209.12349

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