Geometric Brownian motion with affine drift and its time-integral
نویسندگان
چکیده
The joint distribution of a geometric Brownian motion and its time-integral was derived in seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions terms modified Bessel functions. In this paper, we revisit classic result the simple Laplace transform approach connection Heun differential equation. We extend methodology with affine drift show that process can be determined doubly-confluent Furthermore, is from asymptotics solutions. addition, provide an application results for double-confluent equation pricing Asian options. Numerical accuracy efficiency new method.
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2021
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2020.125874