Weak existence of the squared Bessel process and CIR process with skew reflection on a deterministic time dependent curve

TL;DR

This paper constructs the Cox-Ingersoll-Ross (CIR) process and its square root with skew reflection on a time-dependent curve using moving domain techniques and stochastic calculus.

Contribution

It introduces a novel construction of CIR and squared Bessel processes with skew reflection on a dynamic boundary, expanding their theoretical framework.

Findings

Successful construction of CIR process with skew reflection on a time-dependent curve

Extension of moving domain techniques to stochastic processes with boundary reflection

Provides a foundation for modeling interest rates with boundary behaviors

Abstract

Using the technique of moving domains, and classical direct stochastic calculus, we construct the Cox-Ingersoll-Ross process, as well as its square root, with additional skew reflection on a deterministic time dependent curve.