A note on a.s. finiteness of perpetual integral functionals of diffusions

A Characterization of the Finiteness of Perpetual Integrals of Levy Processes

We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-dimensional Lévy processes that drifts to plus infinity. This generalizes previous work of Döring and Kyprianou, who considered Lévy processes having a local time, leaving the general case as an open problem. It turns out, that the criterium in the general situation simplifies significantly in the situation, where the process has a local time, but we also demonstrate that in general our criterium can not be reduced. Th…

Perpetual Integrals for Levy Processes

We ask for necessary and sufficient conditions for almost sure finiteness of the perpetual integrals of a Levy process. Zero-one laws are already known for Brownian motion with drift and spectrally one-sided Levy processes. Under the assumption that local times exist, we use fluctuation theory and Jeulin's lemma to prove the zero-one law.

关于基于积分的百慕大期权定价合理性的简短说明

A brief note on the soundness of Bermudan option pricing via cubature

本文研究基于（高维）积分的迭代百慕大期权定价算法，证明迭代产生的百慕大价格序列有界且单调递增至近似永续百慕大期权价格，收敛速度为线性且折扣因子为收敛因子，并刻画该近似永续价格为迭代过程的最小不动点。