Semiparametric Estimation of Optimal Dividend Barrier for Spectrally Negative L\'{e}vy Process

TL;DR

This paper develops a semiparametric method to estimate the optimal dividend barrier for spectrally negative Lévy processes, using a novel quasi-process approach, and demonstrates its consistency and numerical performance.

Contribution

It introduces a new estimator for the optimal dividend barrier based on shuffling increments, extending existing methods to a broader class of Lévy processes.

Findings

Estimator is consistent for the optimal dividend barrier.

Numerical analysis confirms effectiveness in compound Poisson models.

Method applies to spectrally negative Lévy processes with diffusion perturbations.

Abstract

We disucss a statistical estimation problem of an optimal dividend barrier when the surplus process follows a L\'{e}vy insurance risk process. The optimal dividend barrier is defined as the level of the barrier that maximizes the expectation of the present value of all dividend payments until ruin. In this paper, an estimatior of the expected present value of all dividend payments is defined based on ``quasi-process'' in which sample paths are generated by shuffling increments of a sample path of the L\'{e}vy insurance risk process. The consistency of the optimal dividend barrier estimator is shown. Moreover, our approach is examined numerically in the case of the compound Poisson risk model perturbed by diffusion.