Least squares estimator for path-dependent McKean-Vlasov SDEs via discrete-time observations

TL;DR

This paper develops a least squares estimator for path-dependent McKean-Vlasov SDEs using discrete observations, addressing challenges with irregular coefficients and establishing consistency and asymptotic properties.

Contribution

It introduces a novel contrast function based on a tamed Euler-Maruyama scheme and linear interpolation, applicable to irregular coefficient SDEs with path-dependence.

Findings

Proves consistency of the estimator

Derives the asymptotic distribution

Demonstrates applicability to irregular coefficient SDEs

Abstract

In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown pa- rameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of our paper lie in three aspects: (i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solu- tion; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (e.g., H"older continuous) and path-distribution dependent.