Auto-balanced common shock claim models

TL;DR

This paper introduces 'auto-balanced' common shock claim models ensuring proportional contributions of shocks and idiosyncratic components across observations, with simple conditions for auto-balance and numerical demonstrations.

Contribution

It proposes a new class of auto-balanced models that maintain constant proportional contributions, addressing unbalanced issues in traditional shock models.

Findings

Conditions for auto-balance are simple and widely applicable.

Numerical illustrations demonstrate the effectiveness of the proposed models.

Addresses over- and under-contribution issues in claim triangle models.

Abstract

The paper is concerned with common shock models of claim triangles. These are usually constructed as a linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses 'auto-balanced' models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.