Non-parametric estimators of scaled cash flows

TL;DR

This paper introduces a scaled non-parametric estimator for multi-state life insurance cash flows that handles sampling effects and censoring, demonstrating superior performance and broad applicability.

Contribution

A novel scaled Aalen--Johansen estimator is developed, providing strong theoretical guarantees and improved performance over existing methods in actuarial applications.

Findings

Estimator is strongly consistent and asymptotically normal.

Simulation shows it outperforms previous methods.

Potential applications extend beyond insurance.

Abstract

In multi-state life insurance, incidental policyholder behavior gives rise to expected cash flows that are not easily targeted by classic non-parametric estimators if data is subject to sampling effects. We introduce a scaled version of the classic Aalen--Johansen estimator that overcomes this challenge. Strong uniform consistency and asymptotic normality are established under entirely random right-censoring, subject to lax moment conditions on the multivariate counting process. In a simulation study, the estimator outperforms earlier proposals from the literature. Finally, we showcase the potential of the presented method to other areas of actuarial science.