Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent CKLS and Vasicek Model

TL;DR

This paper establishes log-Harnack inequalities and exponential ergodicity for distribution-dependent CKLS and Vasicek models, extending their mathematical understanding in finance-related stochastic processes with distribution-dependent coefficients.

Contribution

The paper derives new log-Harnack inequalities and ergodicity results specifically for distribution-dependent CKLS and Vasicek models, which were not previously analyzed in this context.

Findings

Proved log-Harnack inequality for distribution-dependent CKLS model.

Established exponential ergodicity for the distribution-dependent Vasicek model.

Extended mathematical tools for analyzing interest rate models with distribution dependence.

Abstract

In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order $\theta$ with $\theta\in[\frac{1}{2},1)$; the other one is Vasicek model, where the diffusion coefficient only depends on distribution. Both models in the distribution independent case can be used to characterize the interest rate in mathematical finance.