Geometric Brownian motion with affine drift and its time-integral

作者：

Highlights：

• Connect the geometric Brownian motion with affine drift to the Heun differential equation.

• The joint distribution of this process and its time-integral can be determined by a doubly-confluent Heun equation.

• The joint Laplace transform of the process and its time-integral is derived from the asymptotics of the solutions.

• Provide an application in pricing Asian options.

摘要

•Connect the geometric Brownian motion with affine drift to the Heun differential equation.•The joint distribution of this process and its time-integral can be determined by a doubly-confluent Heun equation.•The joint Laplace transform of the process and its time-integral is derived from the asymptotics of the solutions.•Provide an application in pricing Asian options.

论文关键词：Doubly-confluent Heun equation,Deometric Brownian motion with affine drift,Lamperti’s transformation,Asymptotics,Boundary value problem

论文评审过程：Received 13 July 2020, Revised 4 November 2020, Accepted 6 December 2020, Available online 18 December 2020, Version of Record 18 December 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125874