2021/10/14 by Joon-Yong Choi, Choi, Joonyong, David Clancy +1 · 1 citation
Economics, Econometrics and Finance · #26A33 #60G17 #60J55 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2110.07639
openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic processes time-changed by an inverse subordinator have been\nsuggested as a way to model the price of assets in illiquid markets, where the\njumps of the subordinator correspond to periods of time where one is unable to\nsell an asset. We develop an excursion theory for time-changed reflected\nBrownian motion and use this to express the price of certain European options\nwith Parisian barrier condition in terms of solutions of a time-fractional PDE.\nWe provide a general description of the occupation measures of time-changed\nprocesses and use this to prove a Ray-Knight theorem for the occupation measure\nof a time-changed Brownian motion with negative drift. We also show that the\nduration of the excursions on finite time intervals obey a Poisson-Dirichlet\ndistribution when a reflected Brownian motion is time-changed by an inverse\nstable subordinator.\n