Non-parametric threshold estimation for classical risk process perturbed by diffusion

TL;DR

This paper develops a non-parametric method to estimate jump sizes and survival probabilities of a risk process observed discretely, addressing the challenge of unobserved jump times and sizes in risk reserve modeling.

Contribution

It introduces a novel non-parametric threshold estimation technique for risk processes with diffusion perturbations based on discrete observations.

Findings

Effective identification of large jumps from discrete data

Accurate estimation of jump sizes and survival probabilities

Applicable to risk processes with diffusion components

Abstract

In this paper,we consider a macro approximation of the flow of a risk reserve, The process is observed at discrete time points. Because we cannot directly observe each jump time and size then we will make use of a technique for identifying the times when jumps larger than a suitably defined threshold occurred. We estimate the jump size and survival probability of our risk process from discrete observations.